A resistance of 4 Ω and a wire of length 5 metres and resistance 5 Ω are joined in series and connected to a cell of e.m.f. 10 V and internal resistance 1 Ω. A parallel combination of two identical cells is balanced across 300 cm of the wire. The e.m.f. E of each cell is:

1. 1.5 V

2. 3.0 V

3. 0.67 V

4. 1.33 V

In the circuit shown here, E₁ = E₂ = E₃ = 2 V and R₁ = R₂ = 4 ohms. The current flowing between points A and B through battery E₂ is 

1. Zero

2. 2 amp from A to B

3. 2 amp from B to A

4. None of the above

The equivalent resistance between the points P and Q in the network given here is equal to (given $r=\frac{3}{2}\Omega$) :

1. $\frac{1}{2}\Omega$

2. 1 Ω

3. $\frac{3}{2}\Omega$

4. 2 Ω

The current in a conductor varies with time t as $I=2t+3t^2$ where I is in ampere and t in seconds. The electric charge flowing through a section of the conductor during t = 2 sec to t = 3 sec is :

1. 10 C

2. 24 C

3. 33 C

4. 44 C

A group of N cells whose emf varies directly with the internal resistance as per the equation E_N = 1.5 r_N are connected as shown in the figure below. The current I in the circuit is 

1. 0.51 A

2. 5.1 A

3. 0.15 A

4. 1.5 A

As the switch S is closed in the circuit shown in the figure, the current passed through it is :

1. 4.5 A

2. 6.0 A

3. 3.0 A

4. Zero

In the circuit shown in figure reading of voltmeter is V₁ when only S₁ is closed, reading of voltmeter is V₂ when only S₂ is closed and reading of voltmeter is V₃ when both S₁ and S₂ are closed. Then

1. V₃ > V₂ > V₁

2. V₂ > V₁ > V₃

3. V₃ > V₁ > V₂

4. V₁ > V₂ > V₃

The V-I graph for a conductor at temperature T₁ and T₂ are as shown in the figure. $(T_2-T_1)$ is proportional to :

(1) $\cos 2\theta$

(2) $\sin \theta$

(3) $\cot 2\theta$

(4) $\tan \theta$

A light bulb, a capacitor and a battery are connected together as shown below with the switch S initially open. When the switch S is closed, which one of the following is true?

1. The bulb will light up for an instant when
    the capacitor starts charging.
2. The bulb will light up when
    the capacitor is fully charged.
3. The bulb will not light up at all.
4. The bulb will light up and go off at regular intervals.

As in figure shown, if a capacitor C is charged by connecting it with resistance R, then energy  given by the battery will be 

1. $\frac{1}{2}C{V}^2$

2. More than $\frac{1}{2}C{V}^2$

3. Less than $\frac{1}{2}C{V}^2$

4. Zero