Two batteries of emf \(\varepsilon_ 1, \varepsilon_ 2\) and internal resistance \(r_1, r_2\) are connected in parallel as shown in figure. The effective emf of the circuit across A and B is: 

1.  \({\varepsilon_1 r_1 + \varepsilon_2 r_2 \over r_1 + r_2 }\)

2.  \({\varepsilon_1 r_2 + \varepsilon_2 r_1 \over r_1 + r_2 }\)

3.  \({\varepsilon_1 r_2 + \varepsilon_2 r_2 \over r_1 \times r_2 }\)

4.  \({\varepsilon_1 r_1 + \varepsilon_2 r_2 \over r_1 - r_2 }\)

$\mathrm{In} \mathrm{the} \mathrm{circuit} \mathrm{shown} \mathrm{in} \mathrm{figure} \mathrm{if} \mathrm{power} \mathrm{dissipated} \mathrm{in} 9\mathrm{\Omega } \mathrm{resistor} \mathrm{is} 144\mathrm{W}, \mathrm{then} \mathrm{potential} \mathrm{difference} \mathrm{across} 3.6\mathrm{\Omega } \mathrm{resistor} \mathrm{will} \mathrm{be}$

1.  36V

2.  18V

3.  9V

4.  Zero

The current \(I\) as shown in the circuit will be:

A meter bridge is set up to determine unknown resistance \(x\) using a standard \(10~\Omega\) resistor. The galvanometer shows the null point when the tapping key is at a \(52\) cm mark. End corrections are \(1\) cm and \(2\) cm respectively for end \(A\) and \(B\). Then the value of \(x\) is:

      
1. \(10.2~\Omega\)
2. \(10.6~\Omega\)
3. \(10.8~\Omega\)
4. \(11.1~\Omega\)

If a resistance coil is made by joining in parallel two resistances each of 20$\Omega$. An emf of 2V is applied across this coil for 100 seconds. The heat produced in the coil is

(1) 20 J

(2) 10 J

(3) 40 J

(4) 80 J

When a piece of aluminum wire of finite length is drawn through a series of dies to reduce its diameter to half its original value, its resistance will become :

(1) Two times

(2) Four times

(3) Eight times

(4) Sixteen times

Masses of 3 wires of same metal are in the ratio 1 : 2 : 3 and their lengths are in the ratio 3 : 2 : 1. The electrical resistances are in ratio

(1) 1 : 4 : 9

(2) 9 : 4 : 1

(3) 1 : 2 : 3

(4) 27 : 6 : 1

A copper wire has a square cross-section, 2.0 mm on a side. It carries a current of 8 A and the density of free electrons is 8 × 10²⁸ m^–3. The drift speed of electrons is equal to 

(1) 0.156 × 10^–3 m.s^–1

(2) 0.156 × 10^–2 m.s^–1

(3) 3.12 × 10^–3 m.s^–1

(4) 3.12 × 10^–2 m.s^–1

Express which of the following setups can be used to verify Ohm’s law 

(1)
(2)
(3)
(4)

The reading of the ammeter as per figure shown is

(1) $\frac{1}{8}A$

(2) $\frac{3}{4}A$

(3) $\frac{1}{2}A$

(4) 2 A