In the circuit shown in figure (1) the charge on C2 is greater than on C1 (2) the charges on C1 and C2 are same (3) potential difference across C1 and C2 are same (4) potential difference across C1 is greater than across C2

Question

In the circuit shown in figure (1) the charge on C2 is greater than on C1 (2) the charges on C1 and C2 are same (3) potential difference across C1 and C2 are same (4) potential difference across C1 is greater than across C2 (A) 1, 2 and 3 are correct (B) 1 and 2 are correct (C) 2 and 4 are correct (D) 1 and 3 are correct

Tardigrade Admin · Accepted Answer

Since there is only one path for the charge flow, capacitors

C_{1}

and

C_{2}

are in series via the cells of

emf E_{1}

and

E_{2}

The net emf in the circuit

E = E_{1} - E_{2} = 12 - 6 = 6 V

The equivalent capacity

C = \frac{C _{1} C _{2}}{C _{1} + C _{2}}

= \frac{4 \times 8}{4 + 8} = \frac{8}{3} μ F

Charge on each capacitor

(q = q_{1} = q_{2})

q = C V = \frac{C _{1} C _{2} ( E _{1} - E _{2} )}{C _{1} + C _{2}} = \frac{8}{3} \times 6 = 16 μ F

For a capacitor

q = C V

or

V = \frac{q}{C}

∴ V_{1} = \frac{q _{1}}{C _{1}} = \frac{q}{C _{1}} = \frac{C _{2} ( E _{1} - E _{2} )}{C _{1} + C _{2}} = \frac{16}{4} = 4 V

V_{2} = \frac{q _{2}}{C _{2}} = \frac{q}{C _{2}} = \frac{C _{1} ( E _{1} - E _{2} )}{C _{1} + C _{2}} = \frac{16}{8} = 2 V

Q. In the circuit shown in figure (1) the charge on C2​ is greater than on C1​ (2) the charges on C1​ and C2​ are same (3) potential difference across C1​ and C2​ are same (4) potential difference across C1​ is greater than across C2​

1, 2 and 3 are correct

1 and 2 are correct

2 and 4 are correct

1 and 3 are correct

Q. In the circuit shown in figure
(1) the charge on $C_{2}$ is greater than on $C_{1}$
(2) the charges on $C_{1}$ and $C_{2}$ are same
(3) potential difference across $C_{1}$ and $C_{2}$ are same
(4) potential difference across $C_{1}$ is greater than across $C_{2}$