A circuit consists of a battery of emf 12 V

PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Electric Circuits · Electric Circuits

Problem

A circuit consists of a battery of emf 12 V, a resistor R=1.2 kΩR=1.2\,\text{k}\Omega, and a network of three capacitors connected between points X and Y as described below. • Capacitor C1=5 μFC_{1}=5\,\mu\text{F} is connected directly between X and Y. • Capacitor C2=4 μFC_{2}=4\,\mu\text{F} is connected in series with capacitor C3=12 μFC_{3}=12\,\mu\text{F}. This series combination is connected between X and Y in parallel with C1C_{1}. All capacitors are initially uncharged. (a) Calculate the equivalent capacitance of the entire capacitor network between X and Y. Show all steps clearly. (b) The switch is closed at t=0t=0, connecting the network, the resistor, and the battery in series. Determine the time constant τ\tau for the charging process. Express your answer with appropriate units. (c) At time t=τt=\tau, determine the potential difference across the entire capacitor network. Justify your answer using the defining property of the time constant in an RC circuit.

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