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title: "An uncharged capacitor of capacitance \\(C\\) and a resistor of resistance \\(R\\) are connected in series with a periodic voltage source \\(\\varepsilon(t)\\). The source voltage alternates between \\(+V_0\\) and \\(0\\) with period \\(T\\), where the half-period is much greater than the circuit time constant (\\(T/2 \\gg RC\\)), such that \\(\\varepsilon(t) = +V_0\\) for \\(0 \\le t < T/2\\) and \\(\\varepsilon(t) = 0\\) for \\(T/2 \\le t < T\\). Which of the following graphs best represents the potential difference across the resistor, \\(V_R(t)\\), as a function of time over one full period \\(0 \\le t \\le T\\)?"
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url: "https://nerd-notes.com/ubq/121615/"
date_modified: "2026-08-23T05:24:26+00:00"
---

# An uncharged capacitor of capacitance \(C\) and a resistor of resistance \(R\) are connected in series with a periodic voltage source \(\varepsilon(t)\). The source voltage alternates between \(+V_0\) and \(0\) with period \(T\), where the half-period is much greater than the circuit time constant (\(T/2 \gg RC\)), such that \(\varepsilon(t) = +V_0\) for \(0 \le t < T/2\) and \(\varepsilon(t) = 0\) for \(T/2 \le t < T\). Which of the following graphs best represents the potential difference across the resistor, \(V_R(t)\), as a function of time over one full period \(0 \le t \le T\)?

An uncharged capacitor of capacitance \(C\) and a resistor of resistance \(R\) are connected in series with a periodic voltage source \(\varepsilon(t)\). The source voltage alternates between \(+V_0\) and \(0\) with period \(T\), where the half-period is much greater than the circuit time constant (\(T/2 \gg RC\)), such that \(\varepsilon(t) = +V_0\) for \(0 \le t < T/2\) and \(\varepsilon(t) = 0\) for \(T/2 \le t < T\). Which of the following graphs best represents the potential difference across the resistor, \(V_R(t)\), as a function of time over one full period \(0 \le t \le T\)?

![A circuit schematic showing a single loop. An alternating square-wave source labeled \(\varepsilon(t)\) is on the left branch. Connected in series on the top branch is a resistor labeled \(R\), followed by a capacitor labeled \(C\) on the right branch. Beside the circuit is an inset graph of source voltage \(\varepsilon\) versus time \(t\) showing a rectangular pulse that equals \(+V_0\) from \(t=0\) to \(t=T/2\) and drops to \(0\) from \(t=T/2\) to \(t=T\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787462665-K6kph7.jpg)

- **A.** Graph A
- **B.** Graph B
- **C.** Graph C
- **D.** Graph D

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121615/*