---
title: "Time Constant (τ) — AP Physics 2 Definition & Exam Guide"
description: "The time constant τ = R_eq·C_eq tells you how fast a capacitor charges (to ~63%) or discharges (to ~37%) in an RC circuit. Central to AP Physics 2 Unit 11."
canonical: "https://fiveable.me/ap-physics-2-revised/key-terms/time-constant"
type: "key-term"
subject: "AP Physics 2"
unit: "Unit 11"
---

# Time Constant (τ) — AP Physics 2 Definition & Exam Guide

## Definition

The time constant τ of an RC circuit is a measure of how quickly a capacitor charges or discharges, defined as τ = R_eq × C_eq. After one time constant, a charging capacitor reaches about 63% of its final charge, while a discharging capacitor drops to about 37% of its initial charge.

## What It Is

The time constant, written as the Greek letter τ (tau), is the single number that sets the pace of everything in an [RC circuit](/ap-physics-2-revised/unit-11/8-resistor-capacitor-rc-circuits/study-guide/Bzx859T2I32htsAl "fv-autolink"). It's defined as **τ = R_eq × C_eq**, where R_eq is the equivalent resistance and C_eq is the [equivalent capacitance](/ap-physics-2-revised/key-terms/equivalent-capacitance "fv-autolink") of the circuit. Multiply ohms by farads and you get seconds, so τ is literally a time.

Here's what that time means. When a capacitor charges, τ is the time it takes the [charge](/ap-physics-2-revised/unit-10/1-electric-charge-and-electric-force/study-guide/E6OYkOGeroCXwgw1 "fv-autolink") to climb from zero to roughly **63%** of its final value. When a capacitor discharges, τ is the time it takes the charge to fall from full to roughly **37%** of where it started. Notice the capacitor never "finishes" at exactly one τ. Charging and discharging are exponential processes that approach their final values asymptotically. A big τ (large resistance or large capacitance) means a slow, lazy circuit. A small τ means the capacitor snaps to its final state almost instantly. Charge, voltage, and current in the circuit all follow exponential curves governed by this same τ.

## Why It Matters

The time constant lives in **Topic 11.8 (Resistor-Capacitor Circuits)** in [Unit 11](/ap-physics-2-revised/unit-11 "fv-autolink") and directly supports learning objective **11.8.B**, which asks you to describe the behavior of circuits containing combinations of [resistors](/ap-physics-2-revised/key-terms/resistor "fv-autolink") and capacitors. The CED calls τ "a significant feature of an RC circuit," and it's the bridge between two pictures you already know. Right after a switch closes, the circuit is in its transient phase and τ tells you how long that phase effectively lasts. Long after, the circuit settles into steady state where the capacitor acts like an open switch. Because τ depends on *equivalent* resistance and capacitance, this topic also forces you to use the series and parallel capacitor rules from **11.8.A**. The exam loves making you combine capacitors first, then compute τ, so the two skills travel together.

## Connections

### [Equivalent capacitance (Unit 11)](/ap-physics-2-revised/key-terms/equivalent-capacitance)

The C in τ = R_eq·C_eq is the equivalent capacitance, not any single capacitor's value. Capacitors in parallel add (C_eq gets bigger, τ gets longer), while capacitors in series combine by inverse sums (C_eq shrinks below the smallest capacitor, so τ gets shorter). Adding a capacitor in series actually speeds up the [circuit](/ap-physics-2-revised/unit-11/2-simple-circuits/study-guide/LROjr9EJ6hjfPDMC "fv-autolink"), which surprises a lot of people.

### [Transient response (Unit 11)](/ap-physics-2-revised/key-terms/transient-response)

The time constant is the clock for the transient phase. The exponential rise or decay of charge, current, and [voltage](/ap-physics-2-revised/key-terms/voltage "fv-autolink") all happen on a timescale set by τ. After about 5τ, the transient is essentially over and you can treat the circuit as settled.

### [Steady state (Unit 11)](/ap-physics-2-revised/key-terms/steady-state)

[Steady state](/ap-physics-2-revised/key-terms/steady-state "fv-autolink") is what the circuit looks like after many time constants have passed. The capacitor is fully charged, no current flows through its branch, and it behaves like a break in the wire. τ tells you how long it takes to get there; steady state describes where you end up.

### [Conservation of charge (Unit 11)](/ap-physics-2-revised/key-terms/conservation-of-charge)

Charge doesn't vanish during charging or discharging, it flows through the resistor at a rate the exponential curve describes. Kirchhoff's junction rule (conservation of charge) is what lets you set up the circuit equations that produce the exponential behavior τ governs.

## On the AP Exam

Time constant questions show up as both calculations and conceptual reasoning. The classic MCQ gives you a resistor and one or more capacitors and asks for τ, which means combining capacitances first. For example, a 10 μF capacitor discharging through a 2 MΩ resistor gives τ = 20 s, and a 6.0 μF, 3.0 μF, and 2.0 μF set in series collapses to 1.0 μF before you multiply by R. Trickier versions run it backward, like telling you that adding a series capacitor cut τ to one-third and asking you to find the new capacitor. On the free-response side, the 2025 FRQ (Q3) asked for a *prediction* of τ for an unknown resistor and parallel-plate capacitor, so be ready to connect τ to experimental design and to capacitor geometry, not just plug into τ = RC. You should be able to compute τ, explain the 63%/37% meaning in words, and predict how changing R or C changes how fast the circuit responds.

## time constant vs steady state

One time constant is NOT the time to fully charge the capacitor. After 1τ, a charging capacitor is only at about 63% of its final value, and the approach to full charge is asymptotic, so it technically never finishes. Steady state is the practical endpoint reached after several time constants (around 5τ is a good rule of thumb), when the capacitor holds essentially its full charge and current through its branch is zero. Think of τ as the pace and steady state as the destination.

## Key Takeaways

- The time constant of an RC circuit is τ = R_eq × C_eq, and its units work out to seconds because ohms times farads equals seconds.
- During charging, one time constant is the time for the capacitor's charge to rise from zero to about 63% of its final value.
- During discharging, one time constant is the time for the charge to fall to about 37% of its initial value.
- Always reduce the circuit to equivalent resistance and equivalent capacitance before computing τ; series capacitors shrink C_eq and shorten τ, while parallel capacitors grow C_eq and lengthen τ.
- A capacitor never reaches exactly 100% charge because the process is exponential, but after roughly five time constants the circuit is effectively at steady state.
- Larger R or larger C means a slower circuit; smaller R or smaller C means the capacitor charges or discharges faster.

## FAQs

### What is the time constant in an RC circuit?

It's τ = R_eq × C_eq, a measure of how quickly the capacitor charges or discharges. After one τ, a charging capacitor is at about 63% of its final charge, and a discharging capacitor is down to about 37% of its initial charge.

### Is the time constant the time it takes a capacitor to fully charge?

No. One time constant gets you to only about 63% of the final charge, and because charging is exponential, the capacitor approaches full charge asymptotically. A common rule of thumb is that after about 5τ the capacitor is essentially fully charged.

### How is the time constant different from steady state?

Steady state is the final condition where the capacitor is fully charged and acts like an open circuit with zero current through its branch. The time constant tells you how quickly the circuit gets there. They're related but answer different questions: τ is about speed, steady state is about the end behavior.

### Why does adding a capacitor in series make the time constant smaller?

Series capacitances combine by inverse sums, so C_eq drops below the smallest individual capacitor. Since τ = R_eq·C_eq, a smaller C_eq means a smaller τ. AP questions exploit this, like one where a series capacitor cuts τ to one-third of its original value.

### What are the units of the time constant?

Seconds. An ohm times a farad equals a second, which is a quick sanity check on your τ calculations. For example, a 10 μF capacitor with a 2 MΩ resistor gives τ = (2 × 10⁶ Ω)(10 × 10⁻⁶ F) = 20 s.

## Related Study Guides

- [11.8 Resistor-Capacitor (RC) Circuits](/ap-physics-2-revised/unit-11/8-resistor-capacitor-rc-circuits/study-guide/Bzx859T2I32htsAl)

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