Current Electricity — Class 12 Physics PYQs

Two wires P and Q are made of the same material. The wire Q has twice the diameter and half the length as that of wire P. If the resistance of wire P is R, the resistance of the wire Q will be
(A) R
(B) R/2
(C) R/8
(D) 2R

A student has three resistors, each of resistance R. To obtain a resistance $\frac{2}{3}R$, she should connect
(A) all the three resistors in series.
(B) all the three resistors in parallel.
(C) two resistors in series and then this combination in parallel with the third resistor.
(D) two resistors in parallel and then this combination in series with the third resistor.

A battery of emf E and internal resistance r is connected to a rheostat. When a current of 2A is drawn from the battery, the potential difference across the rheostat is 5V. The potential difference becomes 4V when a current of 4A is drawn from the battery. Calculate the value of E and r.

Two wires of the same material and the same radius have their lengths in the ratio 2 : 3. They are connected in parallel to a battery which supplies a current of 15 A. Find the current through the wires.
OR
(b) In the circuit three ideal cells of e.m.f. V, V and 2V are connected to a resistor of resistance R, a capacitor of capacitance C and another resistor of resistance 2R as shown in figure. In the steady state find (i) the potential difference between P and Q and (ii) potential difference across capacitor C.

Two batteries of emf's 3V & 6V and internal resistances 0.2 $\Omega$ & 0.4 $\Omega$ are connected in parallel. This combination is connected to a 4 $\Omega$ resistor. Find :
(i) the equivalent emf of the combination
(ii) the equivalent internal resistance of the combination
(iii) the current drawn from the combination

Define resistivity of a conductor. Discuss its dependence on temperature of the conductor and draw a plot of resistivity of copper as a function of temperature.
(b) (i) "A low voltage battery from which high current is required must have low internal resistance." Justify.
(ii) "A high voltage battery must have a large internal resistance." Justify.

A conductor of length l is connected across an ideal cell of emf E. Keeping the cell connected, the length of the conductor is increased to 2l by gradually stretching it. If R and R' are initial and final values of resistance and $v_d$ and $v_d^{\prime }$ are initial and final values of drift velocity, find the relation between (i) R' and R and (ii) $v_d^{\prime }$ and $v_d$.
(ii) When electrons drift in a conductor from lower to higher potential, does it mean that all the 'free electrons' of the conductor are moving in the same direction ?

Electrons drift with speed v${}_d$ in a conductor with potential difference V across its ends. If V is reduced to V/2, their drift speed will become :
(A) v${}_d$/2
(B) v${}_d$
(C) 2 v${}_d$
(D) 4 v${}_d$

In a uniform straight wire, conduction electrons move along + x direction. Let $\vec{E}$ and $\vec{j}$ be the electric field and current density in the wire, respectively. Then :
(A) $\vec{E}$ and $\vec{j}$ both are along + x direction.
(B) $\vec{E}$ and $\vec{j}$ both are along – x direction.
(C) $\vec{E}$ is along + x direction, but $\vec{j}$ is along – x direction.
(D) $\vec{E}$ is along – x direction, but $\vec{j}$ is along + x direction.

Consider the circuit shown in the figure. The potential difference between points A and B is :
(A) 6 V
(B) 8 V
(C) 9 V
(D) 12 V