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

1.	\(\frac{2 R r}{\left(R + r \right)}\)	2.	\(\frac{8R\left(R + r\right)}{\left( 3 R + r\right)}\)
3.	\(2r+4R\)	4.	\(\frac{5R}{2}+2r\)

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

In the shown arrangement of the experiment of the meter bridge if AC corresponding to null deflection of galvanometer is x, what would be its value if the radius of the wire AB is doubled 

(1) x

(2) x/4

(3) 4x

(4) 2x

Seven resistances are connected as shown in the figure. The equivalent resistance between A and B is 

(1) 3 Ω

(2) 4 Ω

(3) 4.5 Ω

(4) 5 Ω

A battery of internal resistance 4Ω is connected to the network of resistances as shown. In order to give the maximum power to the network, the value of R (in Ω) should be :

(1) 4/9

(2) 8/9

(3) 2

(4) 18

In the circuit shown here, the readings of the ammeter and voltmeter are

(1) 6 A, 60 V

(2) 0.6 A, 6 V

(3) 6/11 A, 60/11 V

(4) 11/6 A, 11/60 V

A wire of resistor R is bent into a circular ring of radius r. Equivalent resistance between two points X and Y on its circumference, when angle XOY is α, can be given by

(1) $\frac{R\alpha }{4{\pi }^2}(2\pi -\alpha )$

(2) $\frac{R}{2\pi }(2\pi -\alpha )$

(3) R (2π – α)

(4) $\frac{4\pi }{R\alpha }(2\pi -\alpha )$

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 following circuit, a 10 m long potentiometer wire with resistance 1.2 ohm/m, a resistance R₁ and an accumulator of emf 2 V are connected in series. When the emf of the thermocouple is 2.4 mV then the deflection in the galvanometer is zero. The current supplied by the accumulator will be :

(1) 4 × 10^–4 A

(2) 8 × 10^–4 A

(3) 4 × 10^–3 A

(4) 8 × 10^–3 A