Electric CircuitsSeries and Parallel Circuits

Making Electricity Work for Us

Electric Potential Source◦ battery◦ power supply◦ electrical outlet

Load◦ resistor◦ light bulb◦ appliances

Conductors◦ wires to connect◦ switches

Requirements for a Circuit

+

-

+

-

V

A+

-

Voltmeter◦measures voltage◦voltage across◦wired in parallel

Ammeter◦measures current◦current through◦wired in series

Measuring Voltage and Current

Overloaded Circuit◦Wires connected in a short circuit◦Too many devices in parallel

Current becomes too high◦wires become too hot◦fire danger

Protection shuts off the power◦fuse burns out◦circuit breaker opens

Overloading Circuits

A junction is an “intersection” or area of branching in a circuit.

Junction Rule: The Current (amps) RuleThe current flowing into a junction must equal the current going out of the junction.

Iin = Iout

The Junction Rule

Around any complete loop in a circuit, the voltage gains (from the battery) must equal the voltage drops (through the bulbs).

Vgains = Vdrops

The Loop Rule

+

-

V

R1 R2

R3

Series Circuit

Current has only one way to go through the resistors.

The current through each resistor is the same.

To get the total (or equivalent) resistance, add up the resistance of all the resistors.

The current of the circuit is equal to the supply voltage divided by the total resistance.

Simple Series Circuit

The voltage drop across each resistor is equal to the current times the resistance (V = IR).

The total voltage drop across the resistors is equal to the voltage provided by the supply.

RTOT = R1 +R2 +R3 + …… + RN

Series (continued)

+

-

V R2 R3R1

Parallel Circuit

The voltage is the same across each resistor.

The current splits between resistors. The current will like the easiest path (the least resistance), so there will be more current in the path of the smallest resistor.

The total current in the circuit equals the sum of the currents in the branches.

As the number of parallel branches increases, the overall resistance decreases.

Parallel Circuit

The equivalent resistance of two identical resistors in parallel is one half the value of the individual resistors.

For two resistors that are not the same,

For more than two resistors,

Parallel (continued)

1 2

1 2eq

R RR

R R

1 2 3

1 1 1 1 1...

eq NR R R R R

R2

R3

R4

+

-

V

R1

Complex Circuit

R2

R3

R4

+

-

V

R1

R2R2

R3R3

R4R4

+

-

V

+

-

+

-

V

R1R1

1. Find the parts of the circuit where resistors are simply in parallel or simply in series. In the circuit above, R3 and R4 are simply in series. There are no resistors simply in parallel.

2. If two or more resistors are in series, combine them in an equivalent resistance.

3. If two or more resistors are in parallel, combine them in an equivalent resistance.

4. Repeat steps 1 and 2 until the circuit has been simplified into a single resistance.

5. Determine the current of the simplest circuit. 6. Work back out, calculating the voltage across each

resistor the current through each resistor using Ohm’s Law.

Simplifying Complex Circuits