Question

Q3. A single capacitor of capacitance C1 is connected to a battery. Then a second capacitor of capacitance G2 is added in parallel with C1. Carefully explain all your answers to the following questions. (i) Does the potential difference across C1 increase, decrease, or stay the same, compared to the circuit containing only the battery and C1? (ii) Does the charge q1 on C1 increase, decrease, or stay the same. compared to the circuit containing only the battery and C1? (iii) Is the equivalent capacitance of C1 and C2 larger than C1, smaller than C1, or equal to C1? (iv) Is the charge stored on C1 and C2 together more than, less than. or equal to the charge stored previously on C1? (y) How do you answers to these questions (i)-(iv) change if C2 is connected in series rather than in parallel with C1?

Answer 1

Ponsider the diagram shown below representing two parallel capacitors with a battery source C2 The potential difference is same in the component connected in parallel combinations Therefore, the voltage across the capacitor ssl same with parallel capacitor C compared to the circuit of only capacitor C,

Consider the expression for the charge on the capacitor Here, Q is charge, C is capacitance, and V is voltage. The voltage is same in capacitor. Therefore, the charge on capacitor is also same after 0-CV connecting another capacitor C, in parallel. Consider the equivalent capacitance of the circuit. Here, C is equivalent capacitance. From the above expression, the equivalent capacitance is larger than C (iv) Consider the charge stored previously on C Consider the charge stored on C, and C, together. From the above, Q is more than Q

Hence, the charge stored on C and C together is more than charge stored previously on ers of (i)-(iv) woul Consider the diagram shown below representing two series capacitors with a battery C2 Let the voltage across capacitor C and C are and , respectively Write the expression for the voltage

Hence, the potential difference across C is decreased, compared to the circuit of only capacitor C1. Therefore, the charge on the capacitor C is also decreased. Write the expression for the equivalent capacitance for the series combination. Therefore, the equivalent capacitance is smaller than C This results in low equivalent charge in the circuit than charge stored previously on C