Problem Statement:

We need to find the contribution to the voltage $V_t$ across the resistor $R_2$ from the current source $I_s$ using the principle of superposition.

Given:

• $V_s = 12.58 \, \text{V}$ (voltage source)
• $I_s = 2.26 \, \text{A}$ (current source)
• $R_1 = 19 \, \Omega$
• $R_2 = 9 \, \Omega$

Superposition Principle:

To find the voltage across $R_2$ due to $I_s$ alone, we deactivate the voltage source $V_s$. Deactivating a voltage source means replacing it with a short circuit.

Circuit Simplification:

With $V_s$ replaced by a short circuit, the current $I_s = 2.26 \, \text{A}$ is divided between $R_1$ and $R_2$.

Step 1: Determine the total resistance in the circuit:

The resistors $R_1$ and $R_2$ are in parallel: $R_{total} = \frac{R_1 \times R_2}{R_1 + R_2} = \frac{19 \, \Omega \times 9 \, \Omega}{19 \, \Omega + 9 \, \Omega} = \frac{171}{28} \approx 6.107 \, \Omega$

Step 2: Calculate the voltage across $R_2$:

The voltage across $R_2$ due to the current source $I_s$ is given by Ohm's law: $V_t = I_s \times R_{parallel \, 2}$ where $R_{parallel \, 2}$ is the equivalent resistance as seen by the current source through $R_2$, which is equal to the parallel combination of $R_1$ and $R_2$.

$V_t = 2.26 \, \text{A} \times \left(\frac{171}{28}\right) \approx 13.81 \, \text{V}$

Final Answer:

The contribution to the voltage $V_t$ across $R_2$ from the current source $I_s$ is 13.8 V (rounded to three significant figures).

Would you like further details on this solution or have any other questions? Here are some related questions you might find helpful:

1. How does the superposition principle apply to linear circuits?
2. What happens when a current source is deactivated in a circuit?
3. How can you calculate the equivalent resistance in complex circuits?
4. How does the voltage division rule apply in parallel circuits?
5. What are some common mistakes when applying the superposition theorem?

Tip: When using the superposition principle, always ensure to deactivate all other independent sources one at a time, and then sum the effects for each source to find the total response.