Question 11:
easy3 capacitors each of capacitance \(2\text{ }\mu\text{F}\) are to be connected to obtain an equivalent capacitance of \(3\text{ }\mu\text{F}\). Which of the following combination is possible?
Connecting two \(2\text{ }\mu\text{F}\) capacitors in series gives \(1\text{ }\mu\text{F}\). Adding the third \(2\text{ }\mu\text{F}\) capacitor in parallel to this combination yields \(1 + 2 = 3\text{ }\mu\text{F}\).
Question 12:
easyAssertion (A): When two capacitors of capacitance \(300 \text{ pF}\) and \(600 \text{ pF}\) which can work upto maximum potential of \(4 \text{ kV}\) and \(3 \text{ kV}\) respectively, are connected in series, their combination can work upto maximum potential of \(7 \text{ kV}\).
Reason (R): In series combination, maximum working potential will be sum of maximum working potential of individual capacitors.
For capacitors in series, the maximum charge \(Q_{\text{max}}\) the combination can hold is the minimum of individual \(C V_{\text{max}}\). Here, \(Q_{1, \text{max}}\ = 300 \text{ pF} \cdot 4 \text{ kV} = 1200 \text{ pC}\) and \(Q_{2, \text{max}}\ = 600 \text{ pF} \cdot 3 \text{ kV} = 1800 \text{ pC}\). So, \(Q_{\text{max}}\ = 1200 \text{ pC}\). Equivalent capacitance \(C_{\text{eq}}\ = (300 \cdot 600) / (300 + 600) = 200 \text{ pF}\). The maximum potential for the combination is \(V_{\text{max}}\ = Q_{\text{max}} / C_{\text{eq}}\ = 1200 \text{ pC} / 200 \text{ pF} = 6 \text{ kV}\). Thus, both Assertion (A) and Reason (R) are false.
Question 13:
easyAssertion (A): Two parallel plates having unequal charges have same capacitance as that of equal and opposite charges on same plates and same configuration.
Reason (R): Capacitance of system/ configuration is independent of charge on plates.
A: True. The capacitance of a parallel plate capacitor, \(C = \frac{\epsilon_0 A}{d}\), is a geometric property and does not depend on the specific charge values on the plates, only their configuration.\nR: True. Capacitance is an intrinsic property dependent on geometry and dielectric, not on charge or potential.\n(R) correctly explains (A).
Question 14:
easyAssertion (A): Electrolytic capacitors have larger capacities.
Reason (R): Electrolytic capacitors have a positive and a negative terminal.
Assertion (A) is true; electrolytic capacitors offer high capacitance due to their very thin dielectric layer and large effective plate area. Reason (R) is also true, as all capacitors have two terminals. However, the presence of terminals doesn't explain why they have *larger* capacities, so (R) is not the correct explanation for (A).