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Multiple choice physics effects of electric current thermal effect of electric current heating effect of electric current electric current and its effects

An electric heater operating at $220\ V$ boils $5\ l$ of water in $5\ \text{minutes}$. If it is used on a $110\ V$ line, it will boil the same amount of water in:

  1. $10\ \text{minutes}$

  2. $20\ \text{minutes}$

  3. $5\ \text{minutes}$

  4. $1\ \text{minute}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Heat required to boil the water will be same in the two cases.
Heat produced by heater is:
$Q = \cfrac{V^2}{R} t$
$V^2 = \cfrac{QR}{t}$
$V^2 \propto \dfrac{1}{t}$

$\cfrac{t _2}{t _1} = \cfrac{V _1^2}{V _2^2}$
$t _2 = \dfrac{220^2 \times 5}{110^2}$
$t _2 = 20\ min$
Multiple choice physics effects of electric current thermal effect of electric current heating effect of electric current electric current and its effects

The maximum current $I$, which can be passed through a fuse without melting varies with its radius $r$ as:

  1. $I \propto r$

  2. $I \propto r^{3/2}$

  3. $I \propto r^2$

  4. $I \propto (1/r^2)$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Heat lost per second per unit surface area of fuse wire is
$H = \frac{I^2 \rho }{2 \pi ^2 r^3}$
$\Rightarrow  I^2 \propto r^3$
$\Rightarrow  I \propto r^{\frac{3}{2}}$

Multiple choice physics effects of electric current thermal effect of electric current heating effect of electric current electric current and its effects

If current is flowing through a 10 $\Omega$ resistor, then indicate in which case the maximum heat will be generated?

  1. Current of $5\ A$ flows for $2\ \text{minutes}$.

  2. <span>Current of $4\ A$ flows for $3\ \text{minutes}$.</span>

  3. <span>Current of $3\ A$ flows for $6\ \text{minutes}$.</span>

  4. <span>Current of $2\ A$ flows for $5\ \text{minutes}$.</span>
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Heat produced is given by
$Q = I^2 R t$

Option A:
$5\ A$ flows for $2\ \text{minutes}$
$Q = 5^2 \times 10 \times 2 = 500\ J$

Option B:

$4\ A$ flows for $3\ \text{minutes}$

$Q = 4^2 \times 10 \times 3 = 480\ J$


Option C:
$3\ A$ flows for $6\ \text{minutes}$
$Q = 3^2 \times 10 \times 6 = 540\ J$

Option D:
$2\ A$ flows for $5\ \text{minutes}$
 $Q = 2^2 \times 10 \times 5 = 200\ J$


Hence, option C is correct.

Multiple choice physics effects of electric current thermal effect of electric current heating effect of electric current electric current and its effects

The energy expended in $1\  kW$ electric heater in $30\ \text{seconds}$ will be:

  1. $\displaystyle 3\times 10^4\ J$

  2. $\displaystyle 3\times 10^4\ erg$

  3. $\displaystyle 3\times 10^4\ eV$

  4. $0$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\text{Energy = Power} \times \text{time}$
$\text{Energy} = 1000 \times 30 = 30000\ J = 3 \times {10}^{4}\ J$

Multiple choice physics effects of electric current thermal effect of electric current heating effect of electric current electric current and its effects

A resistor has resistance R. When the potential difference across the resistor is V, the current in
the resistor is I. The power dissipated in the resistor is P. Work W is done when charge Q flows
through the resistor.
What is not a valid relationship between these variables? 

  1. $I =\frac {P}{V}$

  2. $Q =\frac {W}{V}$

  3. $R =\frac {P}{I^2}$

  4. $R =\frac {V}{P}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

We know that 

$P= VI$
$\implies P= V\times \dfrac{V}{R}$
$\implies P = \dfrac{V^2}{R}$
$\implies R= \dfrac{V^2}{P}$..............(1)
Therefore the option D is wrong .

Multiple choice physics effects of electric current thermal effect of electric current heating effect of electric current electric current and its effects

Three heaters each rated 250 W, 100 V are connected in parallel to a 100 V supply. The energy supplied in kWh to the three heaters in 5 hours is :

  1. $3.75 kWh$

  2. $4 kWh$

  3. $0.6 kWh$

  4. $5.74 kWh$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Power is given as: $P=VI$


Substituting, $I=\dfrac{V}{R}$ in the above formula, we get, $P=\dfrac { { V }^{ 2 } }{ R } $

Given that the voltage is $250\ V$ and the power is $60\ W$, the resistance of the bulb is calculated as follows.

$R=\dfrac { { V }^{ 2 } }{ P } =\dfrac { { 100 }^{ 2 } }{ 250 } =40\Omega$

Hence, the resistance of each resistor is 40 ohms.

The energy consumed by the appliance in kWh is given by the formula: $P=\dfrac { { V }^{ 2 } }{ R } \times t=\dfrac { { 100 }^{ 2 } }{ 40 } \times t= 1.25\ kWh$.

When three heater are connected in parallel, then the total energy consumed is given as $1.25\ kWh\times 3=3.75\ kWh.$.

Hence, the total power consumed is 3.75 kWh.

Multiple choice physics effects of electric current thermal effect of electric current heating effect of electric current electric current and its effects

A geyser is rated 1500 W, 250 V. This geyser is connected to 250 V mains. The cost of energy consumed at Rs. 4.20 per kWh for 5 hours will be :

  1. $Rs. 250$

  2. $Rs. 300$

  3. $Rs. 310$

  4. $Rs. 315$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The electric power in watts associated with a complete electric circuit or a circuit component represents the rate at which energy is converted from the electrical energy of the moving charges to some other form, e.g., heat, mechanical energy, or energy stored in electric fields or magnetic fields. 


The power is given by the product of applied voltage and the electric current.

 That is, $P=VI. The\ power\ of\ the\ geyser\ is\ given\ as\ 1500 W$

The energy consumed by the geyser in kWh is given by the formula $Q=P\times t\quad =\quad 1500W\times 50hours\quad =\quad 75\quad kWh$. 

Hence, the energy consumed by the geyser in 5 hours is 75 kWh. 

The cost of energy consumed per kWh is given as Rs. 4.20.

That is, $4.20\times 75\quad kWh=\quad Rs.315$

Hence, the total cost is given as Rs. 315.

Multiple choice physics effects of electric current thermal effect of electric current heating effect of electric current electric current and its effects

A lamp of $100\ W$ and a heater of $1\ kW$ are in simultaneous use for $10\ hrs$. The units of electricity consumed according to the meter in the house is:

  1. $10$

  2. $9$

  3. $11$

  4. $1$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For lamp, electrical energy consumed is $E _L = P _Lt =100\times 10 = 1\ kWh$

For heater, electrical energy consumed is $E _H = P _Ht =1000\times 10 = 10\ kWh$
Hence, total electrical energy consumed is: $E = E _L+E _H=11\ kWh$

Multiple choice physics effects of electric current thermal effect of electric current heating effect of electric current electric current and its effects

A motor of $50\ W$ runs for $20\ hrs$. How many 'units' ($kWh$) of electrical energy are consumed?

  1. $5\ kWh$

  2. <span>$2\ kWh$</span>

  3. <span>$1\ kWh$</span>

  4. <span>$2.5\ kWh$</span>
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given :       $P = 0.050\ kW$ 

                   $t = 20\ h$

Energy consumed,      
$E = Pt =0.050\times 20 = 1\ kWh$