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

In the given circuit, it is observed that the current I is independent of the value of the resistance R₆. Then the resistance values must satisfy 

1. $R_1{R}_2{R}_5=R_3{R}_4{R}_6$

2. $\frac{1}{R_5}+\frac{1}{R_6}=\frac{1}{R_1+R_2}+\frac{1}{R_3+R_4}$

3. $R_1{R}_4=R_2{R}_3$

4. $R_1{R}_3=R_2{R}_4=R_5{R}_6$

The effective resistance between points \(P\) and \(Q\) of the electrical circuit shown in the figure is:

A wire of length L and 3 identical cells of negligible internal resistances are connected in series. Due to current, the temperature of the wire is raised by ΔT in a time t. A number N of similar cells is now connected in series with a wire of the same material and cross–section but of length 2 L. The temperature of the wire is raised by the same amount ΔT in the same time t. The value of N is- 

1. 4

2. 6

3. 8

4. 9

A wire of resistance 10 Ω is bent to form a circle. P and Q are points on the circumference of the circle dividing it into a quadrant and are connected to a Battery of 3 V and internal resistance 1 Ω as shown in the figure. The currents in the two parts of the circle are 

1. $\frac{6}{23}A\text{\hspace{0.17em}\hspace{0.17em}and\hspace{0.17em}\hspace{0.17em}}\frac{18}{23}A$

2. $\frac{5}{26}A\text{\hspace{0.17em}\hspace{0.17em}and\hspace{0.17em}}\frac{15}{26}A$

3. $\frac{4}{25}A\text{\hspace{0.17em}\hspace{0.17em}and\hspace{0.17em}\hspace{0.17em}}\frac{12}{25}A$

4. $\frac{3}{25}A\text{\hspace{0.17em}\hspace{0.17em}and\hspace{0.17em}\hspace{0.17em}}\frac{9}{25}A$

In the circuit element given here, if the potential at point B, V_B = 0, then the potentials of A and D are given as 

1. $V_A=-1.5V,V_D=+2V$

2. $V_A=+1.5V,V_D=+2V$

3. $V_A=+1.5V,V_D=+0.5V$

4. $V_A=+1.5V,V_D=-0.5V$

What is the equivalent resistance between terminals \(A\) and \(B\) of the network?

In the given circuit, with a steady current, the potential drop across the capacitor must be :

1. V

2. V / 2

3. V / 3

4. 2V / 3

An ionization chamber with parallel conducting plates as anode and cathode has \(5\times 10^7\) electrons and the same number of singly-charged positive ions per \(\text{cm}^3.\)  The electrons are moving at \(0.4~\text{m/s}.\) The current density from anode to cathode is  \(4\mu \text{A/m}^2.\) The velocity of positive ions moving towards cathode is :

1. \(0.4~\text{m/s}\)

2. \(16~\text{m/s}\)

3. Zero

4. \(0.1~\text{m/s}\)