Question

Consider a capacitor-charging circuit. Let Q1 be the charge given to the capacitor in a time interval of 10 ms and Q2 be the charge given in the next time interval of 10 ms. Let 10 μC charge be deposited in time interval t1 and another 10 μC charge be deposited in the next time interval t2.
(a) Q1 > Q2, t1 > t2
(b) Q1 > Q2, t1 < t2
(c) Q1 < Q2, t1 > t2
(d) Q1 < Q2, t1 < t2

Answer 1

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Consider a capacitor-charging circuit. Let Q1 be the charge given to the capacitor in a time interval of 10 ms and Q2 be the charge given in the next time interval of 10 ms. Let 10 μC charge be deposited in time interval t1 and another 10 μC charge be deposited in the next time interval t2.

(a) Q1 > Q2, t1 > t2

(b) Q1 > Q2, t1 < t2

(c) Q1 < Q2, t1 > t2

(d) Q1 < Q2, t1 < t2

Answer 2

(b) Q1 > Q2, t1 < t2

Explanation:

1. From the capacitor characteristics we can say that initially time taking for charging of a capacitor is fast. So from the above statement we conclude that t1 < t2.
2. The charge (Q) of the capacitor is $\mathrm{Q}(\mathrm{t})=\mathrm{Q}_{0}(1-\mathrm{e}-\mathrm{t} / \mathrm{RC})$.
3. From the given statement we can assume that t1 = t2.
4. By substituting t1 = t2 in the Charge (Q) equation we can get that Q1 > Q2.

        Where  R = Resistance

                    C= Capacitance.