CBSE Class 12 · 2017 · Delhi · CapacitanceShort Answer

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A 12 pF capacitor is connected to a 50 V battery. How much electrostatic energy is stored in the capacitor? If another capacitor of 6 pF is connected in series with it with the same battery connected across the combination, find the charge stored and potential difference across each capacitor.

Solution

Energy stored in the 12 pF capacitor alone:

U = \frac{1}{2} C V^{2} = \frac{1}{2} \times 12 \times 1 0^{- 12} \times (50)^{2}

U = 1.5 \times 1 0^{- 8} J

In series with the 6 pF capacitor:

\frac{1}{C} = \frac{1}{12} + \frac{1}{6} \Rightarrow C = 4 pF

Charge (same on each):

q = C V = 4 \times 1 0^{- 12} \times 50 = 2 \times 1 0^{- 10} C

Voltage across each:

V_{12} = \frac{q}{12 pF} = \frac{50}{3} V, V_{6} = \frac{q}{6 pF} = \frac{100}{3} V

(sum

= 50 V

CBSE Class 12 Board · 2017 · Delhi · Subjective

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