Question

Three capacitors are connected to a battery as shown in the figure below. Their capacitances are C-3C, C2-C, and C3-5C. (a) What is the equivalent capacitance of this set of capacitors (in terms of C)? (b) State the ranking of the capacitors according to the charge they store, from largest to smallest. (c) Rank the capacitors according to the potential differences across them, from largest to smallest. (d) If C3 is increased, what happens to the charge stored by each of the capacitors? O Q3, Q1, and Q2 increases. Q3 and Q2 increases; Q1 decreases o All charges stay the same. O Q3 and Q1 increases; Q2 decreases. Need Help? Read IR

Answer 1

a) C2 and C3 are in parallel, with effective capacitance, C23 = C2+C3 = 6C

This C23(6C) is in series with C1 (3C). Equivalent Capacitance Ce = (C23)(C1)/(C23+C1) = 2C

b) All the charge passing throufh battery, also passes through C1, but gets divided at junction of C2 and C3. Charge through C2 and C3 is proportional to their capacitance. Hence

Q1>Q3>Q2

c)Potential drop across Capacitors in parallel is same. Hence delta V2 = delta V3

Potential drop across capacitors in series is inversely proportional to capacitance.

C1 = 2C and C23 = 6C, Hence delta V1 > delta V2 / delta V3

Second option is correct.

d) As C3 increase, C23 and Ce increase.

Increase in Ce increase charge through battery as well as Q1.

Increased Q1 , increases delta V1. Since battery voltage is same , delta V2 = delta V3 decrease. Decrease in delta V2 , decreases Q2.

Since Q1 = Q2+Q3, Q3  increase.

Last option is correct.