In an electrical cable, there is a single wire of radius 9 mm of copper. Its resistance is 5 Ω. The cable is replaced by 6 different insulated copper wires, the radius of each wire is 3 mm. Now the total resistance of the cable will be :

(1) 7.5 Ω

(2) 45 Ω

(3) 90 Ω

(4) 270 Ω

Two uniform wires A and B are of the same metal and have equal masses. The radius of wire A is twice that of wire B. The total resistance of A and B when connected in parallel is :

(1) 4 Ω when the resistance of wire A is 4.25 Ω

(2) 5 Ω when the resistance of wire A is 4.25 Ω

(3) 4 Ω when the resistance of wire B is 4.25 Ω

(4) 7 Ω when the resistance of wire B is 4.25 Ω

Twelve wires of equal length and same cross-section are connected in the form of a cube. If the resistance of each of the wires is \(R\), The effective resistance between two diagonal ends \(A\) and \(E\) will be:

1. \(2R\)
2. \(12R\)
3. \(\frac{5}{6}R\)
4. \(8R\)

You are given several identical resistances each of value R = 10 Ω and each capable of carrying maximum current of 1 ampere. It is required to make a suitable combination of these resistances to produce a resistance of 5 Ω which can carry a current of 4 amperes. The minimum number of resistances of the type R that will be required for this job 

(1) 4

(2) 10

(3) 8

(4) 20

The resistance of a wire is 10^–6 Ω per metre. It is bend in the form of a circle of diameter 2 m. A wire of the same material is connected across its diameter. The total resistance across its diameter AB will be

(1) $\frac{4}{3}\pi \times {10}^{-6}\Omega$

(2) $\frac{2}{3}\pi \times {10}^{-6}\Omega$

(3) $0.88\times {10}^{-6}\Omega$

(4) $14\pi \times {10}^{-6}\Omega$

In the figure shown, the capacity of the condenser C is $2\mu F$. The current in 2 Ω resistor is : 

(1) 9 A

(2) 0.9 A

(3) $\frac{1}{9}A$

(4) $\frac{1}{0.9}A$

When the key K is pressed at time t = 0, which of the following statements about the current I in the resistor AB of the given circuit is true?

(1) I = 2 mA at all t

(2) I oscillate between 1 mA and 2mA

(3) I = 1 mA at all t

(4) At t = 0 , I = 2 mA and with time it goes to 1 mA

There are three resistance coils of equal resistance. The maximum number of resistances you can obtain by connecting them in any manner you choose, being free to use any number of the coils in any way is :

(1) 3

(2) 4

(3) 6

(4) 5

If in the circuit shown below, the internal resistance of the battery is 1.5 Ω and V_P and V_Q are the potentials at P and Q respectively, what is the potential difference between the points P and Q 

(1) Zero

(2) 4 volts (V_P > V_Q)

(3) 4 volts (V_Q > V_P)

(4) 2.5 volts (V_Q > V_P)

Two wires of resistance R₁ and R₂ have temperature coefficient of resistance ${\alpha }_1\text{ and }{\alpha }_2$, respectively. These are joined in series. The effective temperature coefficient of resistance is :

(1) $\frac{{\alpha }_1+{\alpha }_2}{2}$

(2) $\sqrt{{\alpha }_1{\alpha }_2}$

(3) $\frac{{\alpha }_1{R}_1+{\alpha }_2{R}_2}{R_1+R_2}$

(4) $\frac{\sqrt{R_1{R}_2{\alpha }_1{\alpha }_2}}{\sqrt{R_1^2+R_2^2}}$