Core Unit III: Electricity
C. Electric Circuits

2. Series and Parallel Circuits

Key Concepts

A series circuit provides only one path for electrons to follow.

The current in all parts of a series circuit has the same magnitude. For n loads connected in series:

I_S = I₁ = I₂ = ....... = I_n

The sum of the decreases in electric potential around a series circuit is equal to the sum of the increases in applied electromotive force.

V_S = V₁ + V₂ + ....... + V_n

The total resistance in a series circuit is equal to the sum of the individual resistances.

R_S = R₁ + R₂ + ....... + R_n

A parallel circuit provides alternate paths for current to follow.

The total current in a parallel circuit is equal to the sum of the current passing through different branches in the circuit. For n loads connected in parallel:

I_P = I₁ + I₂ + ....... + I_n

The drop in potential difference across all branches in a parallel circuit is the same.

V_P = V₁ = V₂ = ....... = V_n

An equivalent resistance can be considered to consist of a single resistance which replaces two or more resistances.

The equivalent resistance in a parallel circuit can be found by:

(The relationships shown above can also be developed using Ohm's Law and Kirchhoff's Laws.)

Most electric circuits use a combination of series and parallel arrangements. Ohm's Law and Kirchhoff's Laws are useful in analyzing these types of circuits.

Learning Outcomes

Students will increase their abilities to:

1. Define the following terms: series circuit, parallel circuit, equivalent resistance.

2. Draw a schematic diagram of a series circuit and a parallel circuit.

3. Recognize and apply mathematical expressions for current, potential difference, and resistance in series and parallel circuits.

4. Determine an equivalent resistance to replace two or more resistors in an electric circuit.

5. Apply an understanding of equivalent resistance in problem solving.

6. Recognize the importance of using Ohm's Law and Kirchhoff's Laws in analyzing electric circuits.

Teaching Suggestions, Activities and Demonstrations

1. Perform an activity to investigate current, potential difference, or resistance in series and parallel circuits.

2. During the winter, demonstrate the correct method of boosting a car battery. After returning to the classroom, investigate the reasons why the battery being boosted must be connected in parallel to another battery. (Make sure that the car batteries are connected properly. An improper connection could result in an explosion.)

3. Compare theoretical values of current, potential difference, and resistance in a circuit with the actual measured values and account for any discrepancies between the theoretical and measured quantities.

4. Students could try to develop the following, for two resistors in parallel:
   

   For students who have trouble working with reciprocals, the above formula, using "product divided by sum" could be used. It only works for two resistors in parallel. Where more than two resistors are in parallel, it becomes more difficult, and less practical, to try to derive similar equations to avoid reciprocals. Use two resistors at a time and apply the above formula, or use the more general formula shown for resistors in parallel shown earlier.