# Slow AC with a capacitor and an inductor

##### Demonstration

A good way to show phase differences in capacitive and inductive circuits.

#### Apparatus and materials

Inductor, e.g. 12 000 turn coil on laminated core

Electrolytic capacitor (500 µF, 15V), see technical note 1

Low frequency AC generator with battery, see technical note 2

DC milliammeter (±2.5 mA)

DC voltmeter (±5 V)

Crocodile clips, 2

#### Health & Safety and Technical notes

1 Electrolytic capacitors should normally be used only on direct voltages of the correct polarity. However, they may work well in these slow AC experiments. The lack of any direct polarizing voltage may cause some deterioration of the dielectric in these capacitors. It is a wise precaution to 'form' the plates before and after use. This is done by connecting the capacitors to DC with a voltage less than or equal to the working voltage of the capacitor and of the correct polarity.

2 A low frequency AC generator consists of a coil of resistance wire, with a rotating pair of contacts. A smooth low-voltage DC supply is connected across the coil of the generator. The metal brushes rotate in contact with the coil and are connected to the AC output terminals, giving an alternating output.

#### Procedure

a Connect 3 V, DC across the input of the low frequency AC generator. Connect the voltmeter across the output. Put the output also through the milliammeter in series with the 500 μF capacitor. Set the pointers of the meters to their centre positions.

b Turn the generator slowly and show the phase difference.

c Repeat with the inductor in place of the capacitor. Observe the phase difference.

#### Teaching notes

1 This demonstration shows that the current to a capacitor leads the supply voltage by 90 degrees. The current through the inductor lags behind the supply voltage. If it is a very large inductor, then this lag will be about 90 degrees. However all inductors have some resistance and the lag may well be less than 90 degrees because the effects of the resistance and the inductance interact.

2 A circuit with resistance, capacitance and inductance could be set up for demonstration, but the phase difference would then be a complicated vector sum.

3 With a resistor, both V and I are positive at the same time and negative at the same time, and so the power at any instant is always positive, Vrms x I rms. With a capacitor or an inductor, the current and voltage are not in phase, and in extreme cases the power might be zero. The energy just surges in and out of the magnetic field of the inductor, or piles up in the field between the plates of the capacitor and then comes pouring back again. An inductor and capacitor connected in parallel will become an oscillator. If interested, look at a tuned circuit such as in a radio.

This experiment was safety-checked in January 2007