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

A 4 μF capacitor and a resistance of 2.5 MΩ are in series with a 12 V battery. The time after which the potential difference across the capacitor is 3 times the potential difference across the resistor is: [Given ln(2)= 0.693] 

1. 13.86 s

2. 6.93 s

3. 7 s

4. 14 s

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 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 \(1~\text{A}\) when the points \(P\) and \(M\) are connected to a DC voltage source. The potential difference  between the points \(M\) and \(N\) is: 

1. \(1.5~\text{V}\)
2. \(1.0~\text{V}\)
3. \(0.5~\text{V}\)
4. \(3.2~\text{V}\)

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 

An electric kettle takes 4 A current at 220 V. How much time will it take to boil 1 kg of water from temperature ${20}^{°}$C? The temperature of boiling water is ${100}^{°}$C

1. 6.3 min

2. 8.4 min

3. 12.6 min

4. 4.2 min

A wire of a certain material is stretched slowly by ten per cent. Its new resistance and specific resistance become respectively 1. .