In an RC circuit while discharging, the graph of log i versus time is as shown by the dotted line in the diagram figure, where i is the current. When the value of the resistance is doubled, which of the solid curve best represents the variation of log i versus time ?

(1) P

(2) Q

(3) R

(4) S

Three identical capacitors are given a charge Q each and they are then allowed to discharge through resistance R₁, R₂ and R₃. Their charges, as a function of time shown in the graph below. The smallest of the three resistance is

(1) R₃

(2) R₂

(3) R₁

(4) Cannot be predicted

The plates of a capacitor are charged to a potential difference of 320 volts and are then connected across a resistor. The potential difference across the capacitor decays exponentially with time. After 1 second the potential difference between the plates of the capacitor is 240 volts, then after 2 and 3 seconds the potential difference between the plates will be 

(1) 200 and 180 V

(2) 180 and 135 V

(3) 160 and 80 V

(4) 140 and 20 V

In the given figure each plate of capacitance C has partial value of charge equal to:

1. CE

2. $\frac{CE{R}_1}{R_2-r}$

3. $\frac{CE{R}_2}{R_2+r}$

4. $\frac{CE{R}_1}{R_1-r}$

In the figure below, what is the potential difference between the point A and B and between B and C respectively in steady state 

(1) $V_{AB}=V_{BC}=100V$

(2) $V_{AB}=75V,V_{BC}=25V$

(3) $V_{AB}=25V,V_{BC}=75V$

(4) $V_{AB}=V_{BC}=50V$

In the circuit here, the steady state voltage across capacitor C is a fraction of the battery e.m.f. The fraction is decided by 

(1) R₁ only

(2) R₁ and R₂ only

(3) R₁ and R₃ only

(4) R₁, R₂ and R₃

A capacitor of capacitance 5 μF is connected as shown in the figure. The internal resistance of the cell is 0.5 Ω. The amount of charge on the capacitor plate is?

(1) 0 μC

(2) 5 μC

(3) 10 μC

(4) 25 μC

In the figure a long uniform potentiometer wire AB is having a constant potential gradient along its length. The null points for the two primary cells of emfs E₁ and E₂ connected in the manner shown are obtained at a distance of 120 cm and 300 cm from the end A. Find (i) $\frac{E_1}{E_2}$and  position of null point for the cell E₁.

How is the sensitivity of a potentiometer increased ?

Using Kirchoffs rules determine the value of unknown resistance R in the circuit so that no current flows through 4 Ω resistance. Also find the potential difference between A and D.

In the circuit shown, the current through the 4 $\Omega$ resistor is 1 A when the points P and M are connected to a DC voltage source. The potential difference  between the points M and N is 

1. 1.5 V 

2. 1.0 V

3. 0.5 V 

4. 3.2 V

A cell can be balanced against 110cm and 100 cm of potentiometer wire, respectively with and without being short-circuited through a resistance of $10 \Omega$. Its internal resistance is 

(1) 1.0 $\Omega$

(2) 0.5 $\Omega$

(3) 2.0 $\Omega$

(4) zero