15.1 – Circuits

An electric circuit is a closed path through which charges (usually electrons) can flow continuously from one terminal of an electric source to the other.

 

Approach to Circuit Analysis

If a circuit is complicated or unusual, you may redraw the circuit to allow easy identification of parallel or series connections:

    1. Draw e.m.f. source (cell or battery) on a single branch (by itself).
    2. Draw all components in parallel branches.
    3. Identify components in series or parallel by tracing the path of the current from the e.m.f. source.
    4. Take note of whether switches are open or closed and if there are any short circuits.
    5. Redraw and simplify the circuit further if necessary to combine resistance of components.
Example 1: Simplifying A Circuit Diagram
Simplify the following circuit:
Example 2: Simplifying A Circuit Diagram
Simplify the following circuit:

 

Removing ammeters and voltammeters also may make it easier to understand the circuit:

Example 3: Simplifying A Circuit Diagram
Simplify the following circuit:

Removing all the meters we get:

It is now very clear that this is just a simple series circuit with no components in parallel.

If we are still interested to find the values on the meters, then marking the diagram like this can seem less confusing.
Reminder
Ammeters and voltmeters don’t take an active part in the circuit. They are only there to get readings of the current and potential difference within the circuit.
Open Circuit

If there is no complete path for the electrons to move around the circuit then we have an open circuit.

Example: Open Circuit
Consider the following circuit with two identical resistors in series:
 This is a closed circuit and all of the meters will be showing non-zero values. e.g:

A1 = A2 = 2.0 A

V1 = V2 = 3.0 V

V3 = 6.0 V

 

If we remove one of the resistors (and do not reconnect the wires) we will end up with the following open circuit:

As there is no complete path for the electrons to flow, the current will be zero at all places. i.e.

A1 = A2 = 0 A

The e.m.f. of the battery does not change and so remains the same. i.e.

V3 = 6.0 V

There is no current flowing through the left-most resistor.So (by applying V=IR) the potential difference across this resistor is zero.

V1 = 0 V

Thus the remaining voltmeter, V2, must be reading the same as the e.m.f. source. i.e.

V2 = 6.0 V

For an open circuit the p.d. across the gap is always equal to the e.m.f. of the source.

 

Short Circuit

If a wire (assumed to have zero resistance) connects across a component then current will only flow through the wire and none will flow through the component.

We say there is a short circuit across the component. As this component has no effect on the circuit it can be considered to not be present in the circuit.

Example: Short Circuit
Consider the following circuit with two identical resistors connected in series:
 This is a closed circuit and all of the meters will be showing non-zero values. e.g:

A1 = A2 = 2.0 A

V1 = V2 = 3.0 V

V3 = 6.0 V

 

If we connect a wire across the right-most resistor we will end up short-circuiting that resistor.

There is no current flowing through the right-most resistor as the short circuit offers a path with zero resistance. So (by applying V=IR) the potential difference across this resistor is zero.

We can think of the circuit as becoming like this:

Thus:

V2 = 0 V

The e.m.f. of the battery does not change and so remains the same. i.e.

V3 = 6.0 V

So, the potential difference across V1 must have increased (sum of all p.d.s around circuit need to add up to the e.m.f. of the source).

V1 = 6.0 V

The larger p.d. across the left-most resistor tells us that there is a larger current flowing through it. (By application of V = IR.)

As the p.d. across the resistor has in fact doubled we know that the current passing’s through it has also doubled. Thus,

 A1 = A2 = 4.0 A

 

Circuit Symbols

You should be familiar with the basic circuit symbols. A summary of all of those that you are likely to come across is listed here.

D.C. Circuits Next >>

 

2025 Physics Lessons