Physics

Current Electricity and Circuits

450 Questions

Current electricity and circuits questions cover resistors, EMF, internal resistance, and power calculations in series and parallel configurations. Solving these builds a strong understanding of electrical principles and circuit analysis. These physics problems are highly relevant for technical and science aptitude tests.

Resistor combinationsPower dissipationEMF and internal resistanceAC circuit analysisOperational amplifiers

Current Electricity and Circuits Questions

Multiple choice physics electric current drift velocity and mobility drift speed drift velocity & mobility

In conducting wire of radius $5 \, mm$, resistivity $\rho = 1.1 \times 10^{-8} \Omega/m$ and current of $5 A$ is flowing. Drift velocity of free electron is $1.1 \times 10^{-3} \, m/s$ find out mobility of free electron.

  1. $1.57 \, m^2$ volt/sec
  2. $1.25 \, m^2$ volt/sec
  3. $1.2 \, m^2$ volt/sec
  4. $2 \, m^2$ volt/sec
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$V _d = \mu E = \mu \dfrac{V}{\ell}$
$V _d = \dfrac{\mu. I R}{\ell} \dfrac{\mu. I _{\rho} \ell}{A \ell} = \dfrac{\mu . I _{\rho}}{A}$
$\mu = \dfrac{V _d . A}{I _{\rho}} = \dfrac{1.1 \times 10^{-3} \times \lambda \times 25 \times 10^{-6}}{5 \times 1.1 \times 10^{-8}}$
$\mu = 1.57 \,  m^2 $ volt/sec.

Multiple choice physics electric current drift velocity and mobility drift speed drift velocity & mobility

A current passes through a resistor. If K$ _1$ and K$ _2$ represent the average kinetic energy of the conduction electrons and the metal ions respectively then

  1. $K _1 < K _2$
  2. $K _1 = K _2$
  3. $K _1 > K _2$
  4. $\text{Any of these three may occur}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Considering law of conservation of momentum ,electrons possess drift velocity which is greater than velocity of ions.  Thus $K _1>K _2$. hence correct option is option C.

Multiple choice physics electric current, potential difference and resistance drift velocity and mobility drift speed drift velocity & mobility

A 2-ampere current flows in a conductor which has $1 \times {10^{24}}$ free electrons per meter. What is their average drift velocity?

  1. $1.25\,m/s$
  2. $125000\,m/s$
  3. $3 \times {10^8}\,m/s$
  4. $1.25 \times {10^{ - 5}}\,m/s$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

We know 
$I = \eta eAV$
$2 = 1 \times {10^{24}} \times 1.6 \times {10^{ - 24}} \times 1 \times v$
$\boxed{v = 1.25\,m/s}$

Multiple choice physics electric current, potential difference and resistance drift velocity and mobility drift speed drift velocity & mobility

Two wires $X$ and $Y$ have the same resistivity but their cross-sectional areas are in the ratio $2 : 3$ and lengths in the ratio $1 : 2$. They are first connected in series and then the parallel to a d.c. source. Find the ratio of their drift speeds of the electrons in the two wires for the two cases.

  1. Series $6 : 2$, Parallel $2 : 1$.
  2. Series $3 : 2$, Parallel $2 : 1$.
  3. Series $5 : 2$, Parallel $2 : 1$.
  4. Series $3 : 2$, Parallel $3 : 1$.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Drift velocity v_d = I / (neA). In series, current I is the same, so v_d is inversely proportional to A. In parallel, voltage V is the same, so I = V/R, where R = rho*L/A. Thus v_d = V / (ne*rho*L). Calculating these ratios yields 3:2 for series and 2:1 for parallel.

Multiple choice physics electric current, potential difference and resistance drift velocity and mobility drift speed drift velocity & mobility

There is a current of 40 amperes in a wire of $10^{-16}m^{2}$ area of cross-section. If the number of free electrons per $m^{3}$ is $10^{29}$, then the drift velocity will be:

  1. $1.25\times 10^{3}$ m/s
  2. $2.50\times 10^{3}m/s$
  3. $2.0\times 10^{6}m/s$
  4. $25\times 10^{6}m/s$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

If L is the length of wire so velocity is given by $v=\dfrac{L}{t}$

Total number of free electrons in the wire, $Q=nqLA$

Current,

$ I=\dfrac{Q}{t} $

$ I=\dfrac{nqLA}{t} $

$ I=nqvA $

$ v=\dfrac{I}{nqA} $

Where, n is the number of electron, $n={{10}^{29}}$

q is the charge of an electron, $q=1.6\times {{10}^{-19\,}}C$

A is area, $A={{10}^{-16}}\,{{m}^{2}}$

I is current, $I=40\,A$

So, drift velocity,

$ v=\dfrac{40}{{{10}^{29}}\times 1.6\times {{10}^{-19}}\times {{10}^{-16}}} $

$ v=25\times {{10}^{6}}\,m/s $

Multiple choice physics electric current drift velocity and mobility drift speed drift velocity & mobility

Which of the following quantities do not change when an ohmic resistor connected to a battery is heated due to the current?

  1. drift speed

  2. resistivity

  3. resistance

  4. number of free electrons
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

We know, for a conductor carrying current,
Drift speed $= neI =ne \dfrac{V}{R}$
Resistivity $= \dfrac {RA}{L}$
where,
$n$ is no. of electrons, 
$e$  is charge on electrons,
$V$  is applied voltage,
$R$  is resistance and 
$A$  and $L$  are area of cross-section and length of resistor.
From above equations it is clear that drift speed, resistivityand resistance of resistor will be affected due to heating of resistor

Multiple choice physics electric current, potential difference and resistance drift velocity and mobility drift speed drift velocity & mobility

The mean free path of electrons in a metal is $44 \times 10 ^ { - 8 } \mathrm { m }$ . Theelectric field which can give on an average 2$e \mathrm { V }$ energy to an electron in the metal will be in units of VIm 

  1. $8 \times 10 ^ { 7 }$
  2. $5 \times 10 ^ { - 11 }$
  3. $8 \times 10 ^ { - 11 }$
  4. $5 \times 10 ^ { 7 }$
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice physics electric current, potential difference and resistance drift velocity and mobility drift speed drift velocity & mobility

When 3 V potential difference is applied a wire of length 0.1 m. having resistivity $1.6 \times 10^{-5}$ $\Omega m$, the electrons started moving. If the electron density in the wire is $6 \times 10^{10} m^{-1}$, the drift speed of electrons is  

  1. $1.94 \times 10^{-6}\ ms^{-1}$
  2. $1.94 \times 10^{-5}\ ms^{-1}$
  3. $1.94 \times 10^{-8}\ ms^{-1}$
  4. $1.94 \times 10^{-7}\ ms^{-1}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice physics electric current, potential difference and resistance drift velocity and mobility drift speed drift velocity & mobility

When a potential difference $V $  is applied across a conductor at a temperature $T,$  the drift velocity of electrons is proportional to

  1. $\sqrt{V}$
  2. $V$
  3. $\sqrt{T}$
  4. $T$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

We know that Drift velocity $v _d = \displaystyle \dfrac{eE}{m} \tau = \dfrac{e}{m} \tau \left ( \dfrac{V}{l} \right ) $ ($\because E = \dfrac{V}{l})$

so for a particular conductor of a particular length the drift velocity will directly depend upon voltage
Hence $v _d \propto V$. option B is correct.

Multiple choice physics electric current, potential difference and resistance drift velocity and mobility drift speed drift velocity & mobility

The drift velocity of electrons in a conducting wire is of the order of $1:mm/s$, yet the bulb glows very quickly after the switch is put on because

  1. the random speed of electrons is very high of the order of $10^{-6}m/s$

  2. the electrons transfer their energy very quickly through collision.

  3. electric field is set up in the wire very quickly, producing a current through each cross section, almost intantaneously

  4. All the above
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Drift velocity $v _d= \frac{eEt}{m}$ so drift velocity is directly proportional  to the electric filed. When switch is on, the filed is quick set up wire  and produce current through wire instantaneously.   

Multiple choice physics electric current, potential difference and resistance drift velocity and mobility drift speed drift velocity & mobility

When there is an electric current through a conducting wire along its length then an electric field must exist

  1. inside the wire but normal to it

  2. inside the wire but parallel to it

  3. outside the wire but normal to it

  4. outside the wire but parallel to it
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

As current is flowing through it , it means charges are flowing along its length therefore heir must be some electric field parallel to the length of the wire. Hence correct option is B.