The circuit shown below provides an illustration of the principle of superposition. The values of the voltage source voltage and current source current and of both resistances can be adjusted using the scrollbars. Also, both of the sources can be removed form the circuit and put back into the circuit by left-clicking the source with the mouse.

The voltage source voltage and current source current are the inputs to this circuit. The voltage and current measured by the meters are the outputs or responses of the circuit.The principle of superposition says that the response of a linear circuit to several inputs working together is equal to the sum of the response of that circuit to the inputs working separately.

In this example, let

- I and V denote the current and voltage measured by the meters when both the voltage source and the current source are in the circuit. That is, I and V, are both responses to V
_{s}and I_{s}working together. - I
_{1}and V_{1}denote the current and voltage measured by the meters when the voltage source, but not the current source, is in the circuit. That is, I_{1}and V_{1}, are both responses to V_{s}working alone. - I
_{2}and V_{2}denote the current and voltage measured by the meters when the current source, but not the voltage source, is in the circuit. That is, I_{2}and V_{2}, are both responses to I_{s}working alone.

The principle of superposition tells us that

For example, use the scrollbars to set I_{s}= 4 A, V_{s} = 20 V, R_{1}=10 Ohms and R_{2}=30 ohms.

- The meters indicate that I=-2.5 A and V=45 V.
- Left-click on the current source to remove it from the circuit. (Notice that the current source is replaced by an open circuit because an open is equivalent to a zero current source.) Now the meters measure I
_{1}and V_{1}because the voltage source, but not the current source, is in the circuit.The meters indicate that I_{1}=0.5 A and V_{1}=15 V. - Left-click on the current source to restore it to the circuit. Once again the meters measure I and V because both the voltage source and the current source are in the circuit. As expected, the meters gain indicate that I=-2.5 A and V=45 V.
- Left-click on the voltage source to remove it from the circuit. (Notice that the voltage source is replaced by a short circuit because a short is equivalent to a zero voltage source.) Now the meters measure I
_{2}and V_{2}because the current source, but not the voltage source, is in the circuit.The meters indicate that I_{2}=-3 A and V_{2}=30 V. - The principle of superposition predicts that . Indeed, this is the case:

- Use the scrollbars to set I
_{s}= 1 A, V_{s}= 40 V, R_{1}=10 Ohms and R_{2}=40 Ohms.- Observe the values of I and V.
- Left-click on the current source to remove it from the circuit. Notice that R
_{1}and R_{2}are**series resistors**and that V_{1}can be calculated using**voltage division**. (See section 3.4 of**Introduction to Electric Circuits, 5e**by R.C. Dorf and J.A. Svoboda.) Observe the values of I_{1}and V_{1}. - Left-click on the current source to restore it to the circuit then left-click on the voltage source to remove it from the circuit. Notice that R
_{1}and R_{2}are**parallel resistors**and that I_{2}can be calculated using**current division**. (See section 3.5 of**Introduction to Electric Circuits**by RC Dorf and JA Svoboda.) Observe the values of I_{2}and V_{2}. - Verify that .

- In Example 5.4-1 of
**Introduction to Electric Circuits, 5e**by R.C. Dorf and J.A. Svoboda, I_{s}= 2 A, V_{s}= 6 V, R_{1}=3 Ohms and R_{2}=6 Ohms. Example 5.4-1 shows that the current in R_{2}is 4/3 A. Equivalently, the voltage across R_{2}is 6 * 4/3 = 8 V. Use the scrollbars to verify this answer. - Use the scrollbars to set I
_{s}= 3 A, R_{1}=10 Ohms and R_{2}=5 Ohms. Predict the value of V_{s}required to make V = 25 V. Use the scrollbar to check your prediction. - Use the scrollbars to set I
_{s}= 0.6 A, V_{s}= 28 V. Predict the value of R_{1}**=**R_{2}required to make V = 20 V. Use the scrollbars to check your prediction. - Use the scrollbars to set R
_{1}= R_{2}= 40 Ohms. Predict the value of I_{s}and V_{s}and required to make V = 20 V and I = 0.1 A. Use the scrollbars to check your prediction.(Hint: Use the principle of superposition to show that .)