A student constructs two otherwise identical RC charging circuits, A and B
PHYSICS · Single correct · AP · Physics 2: Algebra-based · Electric Circuits · Electric Circuits
Problem
A student constructs two otherwise identical RC charging circuits, A and B. Circuit B uses a resistor whose resistance is twice that of the resistor in Circuit A, while the capacitors in both circuits are identical. Immediately after the switches are closed, which statement correctly compares the charging of the capacitor in Circuit B with that in Circuit A?
(a) Circuit B has twice the time constant, so its capacitor takes longer to reach 63\% of its final charge.
(b) Circuit B has half the time constant, so its capacitor reaches 63\% of its final charge in half the time.
(c) Both circuits have the same time constant because the capacitors are identical; however, the capacitor in Circuit B attains only half the final charge since the larger resistor limits the voltage across it.
(d) Circuit B has twice the time constant, yet its capacitor charges faster because the initial current is smaller.