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

The number of dry cells, each of e.m.f. 1.5 volt and internal resistance 0.5 ohm that must be joined in series with a resistance of 20 ohms, so as to send a current of 0.6 amperes through the circuit is 

(1) 2

(2) 8

(3) 10

(4) 12

Two batteries of e.m.f. 4V and 8 V with internal resistances 1 Ω and 2 Ω are connected in a circuit with a resistance of 9 Ω as shown in figure. The current and potential difference between the points P and Q are 

(1) $\frac{1}{3}A\text{\hspace{0.17em}\hspace{0.17em}and \hspace{0.17em}}3V$

(2) $\frac{1}{6}A\text{\hspace{0.17em}\hspace{0.17em}and\hspace{0.17em} }4V$

(3) $\frac{1}{9}A\text{\hspace{0.17em}\hspace{0.17em}and\hspace{0.17em} 9}V$

(4) $\frac{1}{2}A\text{\hspace{0.17em}\hspace{0.17em}and\hspace{0.17em}\hspace{0.17em}}12V$

Four identical cells each having an electromotive force (e.m.f.) of 12V, are connected in parallel. The resultant electromotive force (e.m.f.) of the combination is :

(1) 48 V

(2) 12 V

(3) 4 V

(4) 3 V

Eels are able to generate current with biological cells called electroplaques. The electroplaques in an eel are arranged in 100 rows, each row stretching horizontally along the body of the fish containing 5000 electroplaques. The arrangement is suggestively shown below. Each electroplaques has an emf of 0.15 V and internal resistance of 0.25 Ω 

The water surrounding the eel completes a circuit between the head and its tail. If the water surrounding it has a resistance of 500 Ω, the current an eel can produce in water is about

(1) 1.5 A

(2) 3.0 A

(3) 15 A

(4) 30 A

A capacitor is connected to a cell of emf E having some internal resistance r. The potential difference in steady state across the 

(1) Cell is < E

(2) Cell is E

(3) Capacitor is > E

(4) Capacitor is < E