Domestic electric circuits and safety precautions - class-X

While for half-circle, the value of current is different at different points and for complete cycle its average value is zero.

Frequency of AC mains in India is 50 Hz,similar to most European countries. Whereas USA uses 60 Hz

Parallel circuit configuration limits the amount of power in each circuit and if one circuit breaker goes out, power remains on in the rest of the home.

In an AC circuit, the instantaneous power p = v*i can be negative if the voltage and current have opposite signs, which occurs when the phase difference is between 90 and 270 degrees.

During wiring in our houses , we use the traditional concept of using red colour wire as live , black as neutral and green for earth.
These colour codes are used to distinguish between live , earth and neutral

A power rating of 60 W at 220 V means that when the bulb is operated across a 220 V supply, it consumes electrical energy at the rate of 60 joules per second.

Copper has very low electrical resistivity, making it an excellent conductor for wiring.

The current through a lamp decreases by $1%$ then percentange change power of the lamp is $2%$.

Power, $P = VI$ (power at high temperature) 

A parallel connection is preferred in a household circuit.
The main advantages of the parallel system are that the supply can be tapped at any convenient point in the house; moreover each appliance is operated by a separate fuse. If the fuse blows off, only that appliance is to be checked. This system involves less wiring and is cheaper to set up.

In our every day lives we use electrical energy to do work for us. This electrical energy is provided either by our power company through the outlets in our wall, or we can buy stored electrical energy in the form of batteries. Different electrical appliances use electrical energy at different rates. Power is the rate at which work is done. The power rating of an appliance tells us the rate at which it uses electrical energy. For example, a 1500 watt hair dryer uses 1500 joules of electrical energy per second.
In any electrical appliance their is a simple relationship between the power output of a component, the potential difference across that component, and the current running through it. This is because charge times potential difference is energy, so (charge per unit time) times (potential difference) gives (energy per unit time).
Thus, we have $P=V I.$
Substituting $V=I R$ from ohm's law, the power relationship can be rewritten as $P={ I }^{ 2 }R$. From this formula, the resistance can be calculated.

A voltmeter is an instrument used for measuring electrical potential difference between two points in an electric circuit. A voltmeter is connected in parallel with a device to measure its voltage.
Hence, the statement is false as the voltmeter is connected in parallel to the device in a circuit.

The electric bulb is the glass enclosure around the filament that often contains a vacuum or is filled with a low-pressure noble gas to prevent the filament from burning out due to evaporation at high temperature. The coiled filaments of incandescent lamps are made up of tungsten, a high resistance material that is drawn into a wire .It has both a high melting point (3382 degrees Celsius) and a low pressure which keep it from melting or evaporating too quickly. Supplying electricity through this coiled tungsten wire generates the light. Due to the resistance, it is heated until the wire becomes white-hot. The emission of light by heating the filament wire to white-hot level is known as incandescence. Here, the electrical energy is converted to heat energy by the resistance of the wire.A fused electric bulb has its filament cut, because at higher temperature for a longer period of time, the tungsten filament melts and the flow of electric current stops and the bulb loses its original utility. 
Hence, the statement is true.

According to old convention, live wire was coded by red colour. Hence live wires were covered with red plastic.

A live wire is red on color .The wire had a red plastic covering.

Nichrome is an alloy with high electrical resistance and a high melting point, making it ideal for heating elements in appliances like electric irons.

In power supply system, there are three wires - Phase(live) wire, neutral wire and earth wire. hence there is no any wire named Zero wire . so correct option is option C.

The wire having a black plastic covering is a neutral wire whereas that having a red covering is a live wire.

$ P=VI$

The earth wire is generally black in colour. This statement is false because the earth wire is green in colour.

The wire having a green plastic covering is a earth wire, black plastic covering is a neutral wire whereas that having a red covering is a live wire.

The colour of earth wire is generally green in colour green wire stands for grounding / earthing in an electric circuit.

$I{R}^{2}$ is not the formula for power.

In power distribution system at home, all power enters via electricity meter. This is important to charge the correct amount of electricity bill every month.

The maximum current which can flow through a fuse without melting it is called its rating.
For example a fuse rated at 8 A, can stand current upto 8 A. If current higher than 8 A flows through the fuse, it would melt and circuit gets broken.the rating of a fuse depends upon the thickness of the fuse wire (because length of the wire is fixed). The thicker fuse has higher rating. So, the thickness of the fuse wire in 8 A circuit is more than that of the fuse wire in 5 A circuit.

Voltage drop is the driving force in any electrical circuit. Hence, it is desired to supply same voltage everywhere.

Potential difference between live wire and neutral wire is about 220 V-250 V. which is generally provided for household purposes in homes for electricity. so correct option is C.

The maximum current which can flow through a fuse without melting it is called its rating.
For example a fuse rated at 8 A, can stand current upto 8 A. If current higher than 8 A flows through the fuse, it would melt and circuit gets broken.

In our homes, we receive supply of electric power through a main supply (also called mains), either supported through overhead electric poles or by underground cables. One of the wires in this supply, usually with red insulation cover, is called live wire (or positive). Another wire, with 
black insulation, is called neutral wire (or negative). In our country, the 
potential difference between the two is $220   V$. At the metre-board in the house, these wires pass into an electricity meter through a main fuse. Through the main switch they are connected to the line wires in the house. These wires supply electricity to separate circuits within the house. Often, two separate circuits are used, one of $15   A$ current rating for appliances with higher power ratings such as geysers, air coolers, etc. The other circuit is of 5 A current rating for bulbs, fans, etc. The earth wire, which has insulation of green colour, is usually connected to a metal plate deep in the earth near the house. This is used as a safety measure, especially for those appliances that have a metallic body, for example, electric press, toaster, table fan, refrigerator, etc. The metallic body is connected to the earth wire, which provides a low-resistance conducting path for the current. Thus, it ensures that any leakage of current to the metallic body of the appliance keeps its potential to that of the earth, and the user may not get a severe electric shock.

Old convention colour for live wire is red whereas in new convention live wire is coded by brown colour.

According to new convention, brown colour is coded for live wire, light blue is coded for neutral wire and green or yellow is coded for earth wire.

Either green or yellow is used for earth wires.

Blue, green and brown are used as insulated wired.

Each electrical appliance is provided with three (3) core flexible cables. The insulation on the three wires is of different colours i.e  Brown for live wire, blue for neutral wire and green or yellow for earth wire.

Every electric appliance is marked with it's power and potential difference at which it works. This marking is called rating of an electrical appliances.

SI unit of electric power is Watt
1 Watt = 1  Volt $\times$ 1 ampere.

Cost $=(0.150 kWh) (hr)  \left ( 12 \dfrac {cent}{kWh} \right )= 9 cent
=$0.09$

Rms value of voltage  $V _{rms} =220 $ volts

Electric Bell is not used to convert electric energy into heat energy as there is no  use of heat in functioning of an electric bell.In electric bell electrical energy is used to convert sound energy.First it converts electric energy into mechanical energy and which is used to produce sound energy.

In a house, there are many electrical appliances that have to run independent of each other. If one appliance is turned on or off it should not affect the other appliances. Thus even if a single appliance is taken out of the circuit (turned off / open switched ) the circuit breaks and hence the current cannot flow in the circuit so every thing turns off.

In India, current flowing through wire is A.C and its frequency is $50Hz$ and voltage $220V$.But, Option C said voltage between two wires is 110V110V, which is wrong.

Joule, Kilowatt-hour, and Erg are units of energy. Watt is a unit of power (energy per unit time).

In tree type distribution of electric power, fuses are present only on the distribution board where as in ring type, there is an individual fuse for each appliance. As there is an individual fuse for each appliance in ring type, only faulty appliance will not work and all the other appliances will not be affected. It is easier to install. So, ring type is advantageous than that of tree type. Hence, choice is (4)

As the resistances are connected in series , same current will pass through them.

Two identical batteries of emf E = 2V and internal resistance r = 1 ohm in parallel have an equivalent emf of 2V and internal resistance r_eq = 1/2 = 0.5 ohm. The maximum power is transferred to the load resistance R when R equals the internal resistance of the source, R = r_eq = 0.5 ohm. The maximum power formula is P = E^2 / (4 * r_eq), which evaluates to 2^2 / (4 * 0.5) = 4 / 2 = 2 W.

Using PV = nRT. Initially: pV = (4/M)RT. Finally: pV = (3.2/M)R(T+50). Equating: 4T = 3.2(T+50) => 4T = 3.2T + 160 => 0.8T = 160 => T = 200 K.

First find the resistance of the bulb using R = V^2 / P = 80^2 / 160 = 40 ohms, and its rated current I = P / V = 160 / 80 = 2 A. When connected across a 100 V supply, the total impedance Z of the bulb and inductor in series is Z = V_total / I = 100 / 2 = 50 ohms. Since Z^2 = R^2 + X_L^2, we get 50^2 = 40^2 + X_L^2, which gives X_L = 30 ohms.

Resistance R = V^2/P. Since V is constant, R is inversely proportional to P. Ratio R1:R2 = P2:P1 = 100:60 = 5:3.

Resistance R = V^2/P = 220^2/100 = 484 Ohm. Power dissipated at 110V = V'^2/R = 110^2 / 484 = 12100 / 484 = 25 W.

This is a complex thermal physics problem involving heat input and heat loss through the walls. The expression in option A correctly models the logarithmic time dependence for heating a system with losses.

Power loss in a line is calculated using the formula P = I^2 * R. First, find current I = P / V = 2200 W / 22000 V = 0.1 A. Then, P_loss = (0.1)^2 * 10 = 0.01 * 10 = 0.1 W.

Microwave oven act on the principle of transferring electron from lower 

Resistance is given by R = rho * (l / A), where A = pi * r^2. Resistance is directly proportional to length (l) and inversely proportional to the square of the radius (r^2). Option C has a large length and the smallest radius, leading to the highest resistance.

The power radiated by a black body is given by the Stefan-Boltzmann law: P = emissivity * sigma * Area * T^4. Plugging in the values: 0.35 * 5.7e-8 * (0.5e-4 m^2) * (3000)^4. Calculating this yields approximately 80.8 W.

Direct Current (DC) is characterized by a constant flow of charge in one direction, meaning it does not oscillate. Therefore, its frequency is zero.

Bulbs used for decoration purposes are connected end to end, that is, in series. This ensures that same amount of current flows through them and the voltage divides across the bulbs as required for low voltage operation. Thus when one bulb goes out, due to being in series, all the bulbs stop glowing.

A geyser is a high-power heating appliance, typically rated at 1000-2000 W. Tubelights, TVs, and fans are low-power devices, usually consuming significantly less energy.

Energy ($power\times time$) is measured in Joules and by including time (t) in the power formulae, the energy dissipated by a component or circuit can be calculated.

Power, $P=VI$
For a $1500\ W$ geyser rated for $250\ V$, the current through is given as $I=\dfrac { P }{ V } =\dfrac { 1500 }{ 250 } =6A$
Hence, the current flowing through the heater is $6\ A$.

The electric bulb is the glass enclosure around the filament that often contains a vacuum or is filled with a low-pressure noble gas to prevent the filament from burning out due to evaporation at high temperature. The coiled filaments of incandescent lamps are made up of tungsten, a high resistance material that is drawn into a wire. It has both a high melting point (3382 degrees Celsius) and a low pressure which keep it from melting or evaporating too quickly. Supplying electricity through this coiled tungsten wire generates the light. Due to the resistance, it is heated until the wire becomes white-hot. The emission of light by heating the filament wire to white-hot level is known as incandescence. Here, the electrical energy is converted to heat energy by the resistance of the wire. A fused electric bulb has its filament cut, because at higher temperature for a longer period of time, the tungsten filament melts and the flow of electric current stops and the bulb loses its original utility. 
Hence, the statement is false.

Power is given as: $P=VI$

Household electrical appliances are always joined in parallel.

When many appliances are switched on simultaneously, a lot of current flows through the main circuit and the current may exceed the permissible amount. This causes overloading and may cause a fire. Thus many electrical appliances should not be used simultaneously.

Answer is A.

The electrical resistance of a wire would be expected to be greater for a longer wire, less for a wire of larger cross sectional area, and would be expected to depend upon the material out of which the wire is made.The resistance of a wire can be expressed as $R=\rho \frac { L }{ A } $, 
where,
$\rho $ - Resistivity  - the factor in the resistance which takes into account the nature of the material is the resistivity
L - Length of the conductor
A - Area of cross section of the conductor.
From this relation, we observe that the length is directly proportional to the resistance and the area of cross section is inversely proportional to the resistance.
In this case, the length of the nichrome coil is reduced due to the burn and so the resistance will also be reduced proportionally. 
When the resistance is decreased, more current flows through the coil and apparently, more power is consumed by the heater as power consumed P = VI.
Hence, the power it will consume now is more than 1 kW.

Answer is A.

If a certain amount of power is dissipated for a given time, then energy is dissipated. Energy (powertime) is measured in Joules and by including time (t) in the power formulae, the energy dissipated by a component or circuit can be calculated.
Energy dissipated = Pt .
In this case, the power dissipated is 1.5 kW and it runs for 8 hours a day.
So, in a day, the energy dissipated is 1.5 * 8 = 12 Kwh.
For 30 days, the power dissipated is 12 * 30 = 360 Kwh.
Hence, the electrical energy is consumed by the air conditioner in 30 days is 360 Kwh.

In this case, the washing machine that is rated $ 300\ W$ is operated for $1$ hr/day. The electric bill has to be calculated for the month of March. That is, the total number of hours the washing machine is operated in this month is $31$ hours as this month has $31$ days.
The total energy that is used by the washing machine in a day is given by the formula $Q=Pt$.
Here, the power is $300\ W$ and the time used is $1\ hour$.
So, $Q=300W\times 1h=300Wh= 0.3\ kWh$
Therefore, the total number of $kWh$ for a month is $0.3kWh\times 31=9.3\ kWh $
The cost of $1\ kWh$ is given as $Rs. 3$.

Answer is B.

The RMS (Root mean square) value tells us what equivalent DC voltage we would need to get the same power, for the neon bulb to glow.
In this case, the neon bulb glows at 50 V ac voltage. Therefore, for the bulb glow with dc voltage, $50\times \sqrt { 2 }  =50\times 1.414=70V$ dc voltage should be applied.
Hence, the neon bulb will flash at 70 V dc.

Components connected in series are connected along a single path, so the same current flows through all of the components. The current through each of the components is the same, and the voltage across the circuit is the sum of the voltages across each component.
When two bulbs are connected in series the first bulb will receive more current. As the bulb has its own resistance, less current will flow to the next bulb.
Hence the first bulb will glow more.

Black, Red and Blue are used for hot wires and White is used as the neutral wire in a 120/208 V circuit. Brown, Orange and Yellow are used as hot wires and gray is used as the neutral wire in a 277/480 V. For grounding, regardless of the voltage, Green is used.The wire having a green plastic covering is a earth wire.

Given: resistors A and B connected in series to a $6V$ battery of $3\Omega$ internal resistance. The sequence of the colour bands on resistor. A is yellow, violet and brown while that on resistor B is red, violet and black respectively. 

1 unit of electric energy is equal to

The wire has a red plastic covering is a live wire. Red wire signifies the phase in an electric circuit. It is the live wire that cannot be connected to another red or bulb wire Red is used in some types of the switch leg.

Total time for which the fan is used $= (10 hours) \times (30 days) = 300$ hours.
Energy consumed $= (80 W) \times (300$ hours$)$
$= 24,000 Wh = 24 kWh.$
But $1 kWh =1$ unit.
Therefore, $24 kWh = 24$ units
The cost of this power $= 24$ units $\times Rs. 3= Rs. 72.00.$

Black, Red and Blue are used for hot wires and White is used as the neutral wire in a 120/208 V circuit. Brown, Orange and Yellow are used as hot wires and gray is used as the neutral wire in a 277/480 V. For grounding, regardless of the voltage, Green is used.The wire having a black plastic covering is a neutral wire.

First two colours says about significant digits of resistance and the third colour gives multiplier.

Given,
Power of the oven $(P) = 2kw = 2 \times 103 W$
Voltage supplied $(V) = 220V$
Current $(I) = ? A$
Power $= V \times I$
$\Rightarrow I = P/V = 2 \times 103/220 = 9.09 A$
Since the domestic electric circuit has a current rating of 5A, the flow of 9.09 A by the Oven exceeds the safe limit. Here, fuse will blow and break the circuit.

Distribution box in domestic electrical circuit provides isolation between appliances and allow them to work paralelly. It also ensures failure in one part do not affect the functioning of the other.

One of the wires in this supply, usually with red insulation cover, is called live wire (or positive). Another wire, with black insulation, is called neutral wire (or negative). In our country, the potential difference between the two is $220   V$. At the metre-board in the house, these wires pass into an electricity meter through a main fuse. Through the main switch they are connected to the line wires in the house. These wires supply electricity to separate circuits within the house. Often, two separate circuits are used, one of $15   A$ current rating for appliances with higher power ratings such as geysers, air coolers, etc. The other circuit is of 5 A current rating for bulbs, fans, etc. The earth wire, which has insulation of green colour, is usually connected to a metal plate deep in the earth near the house. This is used as a safety measure, especially for those appliances that have a metallic body, for example, electric press, toaster, table fan, refrigerator, etc. The metallic body is connected to the earth wire, which provides a low-resistance conducting path for the current. 

$P = VI$
  $= 220 \times 5 = 1100  W$.

Voltage in primary coil     $V _p = 220$ V

The usage of parallel arrangement in domestic circuits has many advantages.

• Each circuit will have the same potential difference which is equal to  the potential difference of the supply line. As a result, each electrical appliance will work under constant voltage.
• When two or more appliances are used at the same time, each appliance will be able to draw the current as needed. The appliances having low resistance will draw higher current and vice versa.
• When distribution circuits are in parallel, then each circuit operates separately. So, if one of the distribution circuits gets overloaded, only the fuse in that circuit will be blown off. The other distribution circuits will remain unaffected.

Answer is B

Fuses are safety devices that are to be built into our electrical system. If there were no fuses and we operated too many appliances on a single circuit, the cable carrying the power for that circuit would get extremely hot, short circuit, and possibly start a fire. To prevent electrical overloads, fuses are designed to trip or blow, stopping the flow of current to the overloaded cable.

Fuse is a piece of wire of a material with a very low melting point. When a high current flow through the circuit due to overloading or short circuit, the wires gets heated and melts. As a result, the circuit is broken and current stops flowing.

The fuse must always be connected to the mains and it must be of correct value. For example, a 15-ampere fuse should trip when the current through it exceeds 15 amperes. A 20-ampere fuse should blow when the current through it exceeds 20 amps.

Given,

In a DC motor, the back emf is proportional to the speed of the motor (E_b = k * omega). The armature current is given by I_a = (V - E_b) / R_a. When the motor has just started, its speed is zero, so the back emf is zero, resulting in the maximum possible armature current.

As the line has some resistance $(R , \neq , 0)$. Also, line that draws power supply has some inductance and capacitance, hence voltage and
current differ in phase $\phi$ such that $|\phi| , < ,
\dfrac{\pi}{2}$.

For Domestic circuits parallel arrangement is always used because:

1. In parallel circuits, if one electrical appliance stop working due to some effect then all other appliances keep working normally.
2. In parallel circuit, each electrical appliance has own switch due to which it can be turn off or on independently, without effecting  other appliances.
3. In parallel circuits, each electrical appliance gets same voltage as that of the power supply line.
4. In the parallel connection of electrical appliances, the overall resistance of the house hold circuit is reduced due to which the current from the power supply is high.

$P=\dfrac { { V }^{ 2 } }{ R } \ R=\dfrac { \rho l }{ A } \ \therefore P=\dfrac { { V }^{ 2 }A }{ \rho l } $

During wiring in our houses , we use the traditional concept of using red color wire as live , black as neutral and green for earth. These color codes are used to distinguish between live, neutral and earth wires, which is a standard coding of color nowadays.

$15   A$ current rating is used for appliances with high power rating such as washing machines, geysers, air coolers etc.

When connected in parallel each bulb has maximum potential difference across it. So, bulb will show its maximum power.

During wiring in our houses , we use the traditional concept of using red color wire as live , black as neutral and green for earth.These color codes are used to distinguish between live, neutral and earth. which is a standard way of coding of colors for electric connections.

According to new convention, live wire of codded by brown colour, neutral wire is coded by light blue colour whereas earth wire is coded by green and yellow colour.

Electric circuits are connected parallely so that if there is problem in any circuit the other circuit does not get affected.