Question

Capacitors of capacities C₁, C_2, and C₃ are connected in series. If the combination is connected to a supply of 'V' volt, then the potential difference across capacitor C₁ is ______

विकल्प

• `(C_2C_3 + C_1C_3 + C_1C_2)/(C_2C_3V)`

• `V/(C_1 + C_2 + C_3)`

• `(C_2C_3V)/(C_2C_3 + C_1C_3 + C_1C_2)`

• `(C_1C_2C_3)/V`

Answer 1

Capacitors of capacities C₁, C_2, and C₃ are connected in series. If the combination is connected to a supply of 'V' volt, then the potential difference across capacitor C₁ is `underline((C_2C_3V)/(C_2C_3 + C_1C_3 + C_1C_2))`

Explanation:

If C is the equivalent capacitance, then `1/C = 1/C_1 + 1/C_2 + 1/C_3`

∴ `1/C = (C_2C_3 + C_1C_3 + C_1C_2)/(C_1C_2C_3)`

∴ C = `(C_1C_2C_3)/(C_2C_3 + C_1C_3 + C_1C_2)`

The charge stored by the combination and the charge on each capacitor is given by

Q = CV = `(C_1C_2C_3V)/(C_2C_3 + C_1C_3 + C_1C_2)`

∴ P.D. across C₁ is given by

`V_1 = Q/C_1 = (C_2C_3V)/(C_2C_3 + C_1C_3 + C_1C_2)`