11.3a - RC Circuits

An RC circuit is a circuit with both a resistor (R) and a capacitor (C). RC circuits are freqent element in electronic devices. They also play an important role in the transmission of electrical signals in nerve cells.

A capacitor can store energy and a resistor placed in series with it will control the rate at which it charges or discharges. This produces a characteristic time dependence that turns out to be exponential. The crucial parameter that describes the time dependence is the "time constant" R C .

The diagram above utilizes a two-pole switch. This allows the user to switch between the charging circuit (Pole A) and discharging circuit (Pole B) with only one switch.

RC Circuit Set-up

An RC Circuit typically has two 'loops'. One can be considered the 'Charging Loop / Circuit' and the second a 'Discharging Loop / Circuit'. Two SWITCHES are sometimes used for this type of circuit, one to control each circuit.

Charging Circuit

During the 'Charging of the Capacitor', the switch of the charging circuit is closed, and the discharging circuit switch is open. This allows a charge to build up on the capacitor. The diagram above shows the common convention flow of current ( + -> -- ).

Discharging Circuit

During the 'Discharging of the Capacitor' the switches are reversed. This allows the charges that are stored in the capacitor to be discharged through the resistive load (Resistor_2). The diagram above shows the common convention flow of current ( + -> -- ).

RC Circuit Data Collection

How does the size of the capacitor (Farads) and the size of the resistor (Ω) effect the rate of charge and discharge of the capacitor.

Use the circuit set up pictured above.
Use a Vernier Voltage sensor (X) to collect the changes in voltage within the capacitor as it charges and discharges.
Repeat your data collection with a second Voltage sensor (Y) to measure the changes in voltage across the resistor as the capacitor either charges or discharges.
Describing the two distinct curves:
- The charging of a capacitor needs to only be described GRAPHICALLY. (How would changing the size of the resistor effect the charging curve?)
- The DIScharging of a capacitor needs to be described both GRAPHICALLY and QUANTITATIVELY.
Compare the τ value from your data to the calculated value based on the capacitor and resistor (τ = the time constant).

Sample MC Question

The circuit diagram shows a capacitor that is charged by the battery after the switch is connected to terminal X. The cell has emf V and internal resistance r. After the switch is connected to terminal Y the capacitor discharges through the resistor of resistance R.

What is the nature of the current and magnitude of the initial current in the resistor after the switch is connected to terminal Y?

Sample Time Constant Problem

A heart defibrillator is used to resuscitate an accident victim by discharging a capacitor through the trunk of her body. A simplified version of the circuit is shown to the right.

(a) What is the time constant if an 8.00-μF capacitor is used and the path resistance through her body is 1.00×103 Ω? 𝜏=𝑅𝐶=(1.00×103Ω)(8.00𝜇𝐹)=8.00ms.

(b) If the initial voltage is 10.0 kV, how long does it take to decline to 5.00×102 V?