In the adjoining circuit, the battery E₁ has an e.m.f. of 12 volts and zero internal resistance while the battery E has an e.m.f. of 2 volts. If the galvanometer G reads zero, then the value of the resistance X in ohm is 

(1) 10

(2) 100

(3) 500

(4) 200

The magnitude and direction of the current in the circuit shown will be 

(1) $\frac{7}{3}$A from a to b through e

(2) $\frac{7}{3}$A from b to a through e

(3) 1A from b to a through e

(4) 1A from a to b through e

n identical cells each of e.m.f. E and internal resistance r are connected in series. An external resistance R is connected in series to this combination. The current through R is 

(1) $\frac{nE}{R+nr}$

(2) $\frac{nE}{nR+r}$

(3) $\frac{E}{R+nr}$

(4) $\frac{nE}{R+r}$

Two identical cells send the same current in 2 Ω resistance, whether connected in series or in parallel. The internal resistance of the cell should be 

(1) 1 Ω

(2) 2 Ω

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

(4) 2.5 Ω

Two non-ideal identical batteries are connected in parallel. Consider the following statements :

(i) The equivalent e.m.f. is smaller than either of the two e.m.f.s

(ii) The equivalent internal resistance is smaller than either of the two internal resistances

(1) Both (i) and (ii) are correct

(2) (i) is correct but (ii) is wrong

(3) (ii) is correct but (i) is wrong

(4) Both (i) and (ii) are wrong