Two resistances R₁ and R₂ are made of different materials. The temperature coefficient of the material of R₁ is α and of the material of R₂ is –β. The resistance of the series combination of R₁ and R₂ will not change with temperature, if R₁/ R₂ equals :

(1) $\frac{\alpha }{\beta }$

(2) $\frac{\alpha +\beta }{\alpha -\beta }$

(3) $\frac{{\alpha }^2+{\beta }^2}{\alpha \beta }$

(4) $\frac{\beta }{\alpha }$

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 cm³. The electrons are moving at 0.4 m/s. The current density from anode to cathode is $4\mu A/m^2$. The velocity of positive ions moving towards cathode is :

(1) 0.4 m/s

(2) 16 m/s

(3) Zero

(4) 0.1 m/s

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

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

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

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

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) $R_1{R}_3=R_2{R}_4=R_5{R}_6$

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

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

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

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

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) $V_A=+1.5V,V_D=-0.5V$

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