## Wednesday, August 20, 2014

### Lab Activity: Series RC Circuit Behavior

Purpose: Observe general behavior of RC circuits before getting into the details in class. We'll look at both charging and discharging cases.

General Setup: You’ll have a power supply, some resistors, a large capacitor, and some multimeters. Set up a circuit with the power supply, resistor and capacitor all in series with each other.

Case A – Small resistance
• Connect a 10-ohm resistor in the circuit with the power supply set to zero.  Make sure there is no initial potential difference across the capacitor.
• With one person measuring the potential difference of the capacitor and another measuring the potential difference of the resistor, quickly turn up the voltage of the power supply (to ~10 V or so).  Write down observations below:
What happens to the voltage across the capacitor?

What happens to the voltage across the resistor?

Try to explain what you think is physically happening in the circuit based on your observations:

Sketch graphs of VCap vs. time, VR vs. time, and I vs. time, as the capacitor charges. *Challenge: What function might produce each graph? Try to guess before we find the details!

• When the voltage across the capacitor is a maximum, how much charge is it storing?  Use your max. voltage measurement.

• When the voltage across the capacitor is a maximum, how much energy is it storing? U = ½ QV = ½ CV2.

• Calculate the product RC.  This actually has units of time and is called the time constant of the circuit.  Show that (ohms)(farads) = seconds.

Quickly turn off the power supply.  What happens to the voltage across the capacitor?
What happens to the voltage across the resistor?  Explain what you think is happening now, and sketch graphs of VCap vs. time, VR vs. time, and I vs. time, as it discharges.

## Case B – Large resistance

• Measure the resistance of the other resistor: __________ W. Connect it in the circuit with the power supply set to zero.  Make sure there is no initial potential difference across the capacitor.
• With one person measuring the potential difference of the capacitor and another measuring the potential difference of the resistor, quickly turn up the voltage of the power supply (to ~10 V or so).  Write down observations below:

What happens to the voltage across the capacitor?

What happens to the voltage across the resistor?

Is there anything different compared to your first circuit?  If so, what? Think rates.

Try to explain what you think is physically happening in the circuit based on your observations:

• Calculate the time constant, RC.  Based on the two circuits you have observed, interpret what the value of the time constant of the circuit refers to.

Wait a couple minutes to let the voltage build up on the capacitor.  Quickly turn off the power supply.  What happens to the voltage across the capacitor?

What happens to the voltage across the resistor?  Explain what you think is happening now.

Theory into Reality: (wait until we do this type of calculation in class)
What is the equation we derived for charge as a function of time for a charging capacitor?

For the first circuit (10-ohm resistor), how much charge is on the capacitor after 0.05 seconds?  After 0.5 seconds?

What is the equation we derived for charge as a function of time for a discharging capacitor?

When the capacitor discharges, how long does it take to lose 25% of its original charge?