Use the Principle of Superposition to determine the absolute value of total current, in milliamperes,
through R in the circuit below, given:
1
E = 39 V, E = 33 V, and R = 17 Ω
2
1
(Round your FINAL answer to a whole number.

The **Principle of Superposition** states that in a linear circuit with multiple independent sources, the total current through any element is the algebraic sum of the currents produced by each source acting alone, while all other independent sources are replaced by their internal resistances (voltage sources are replaced with short circuits, and current sources with open circuits).

### **Given Data:**
- \( E_1 = 39V \)
- \( E_2 = 33V \)
- \( R = 17 \Omega \)

### **Step 1: Effect of \( E_1 \) Alone**
When \( E_1 \) is acting alone, we replace \( E_2 \) with a short circuit.

\[
I_1 = \frac{E_1}{R} = \frac{39V}{17\Omega}
\]

\[
I_1 = 2.2941A
\]

### **Step 2: Effect of \( E_2 \) Alone**
When \( E_2 \) is acting alone, we replace \( E_1 \) with a short circuit.

\[
I_2 = \frac{E_2}{R} = \frac{33V}{17\Omega}
\]

\[
I_2 = 1.9412A
\]

### **Step 3: Finding Total Current (Magnitude)**
The **direction** of each current determines whether they add or subtract. If they are in the same direction, they add; otherwise, they subtract. Assuming the sources are in opposite directions:

\[
I_{\text{total}} = |I_1 - I_2| = |2.2941A - 1.9412A|
\]

\[
I_{\text{total}} = 0.3529A
\]

### **Step 4: Convert to Milliamperes**
\[
I_{\text{total}} = 0.3529A \times 1000 = 353 \text{ mA}
\]

### **Final Answer:**
\[
\mathbf{353 \text{ mA}}
\]

---

Would you like a step-by-step verification or any clarifications?

### **Related Questions:**
1. How does the principle of superposition apply to circuits with resistors and capacitors?
2. What happens if the resistances in the circuit were different for each voltage source?
3. How would the answer change if one of the voltage sources was reversed?
4. Can this method be used for non-linear circuits?
5. How does replacing a voltage source with a short circuit affect the circuit?

### **Tip:**  
Always ensure that when using the superposition principle, each independent source is considered separately while the others are replaced with their internal impedances.

Use the Principle of Superposition to determine the absolute value of total current, in milliamperes, through R in the circuit below, given: E = 39 V, E = 33 V, and R = 17 Ω. (Round your FINAL answer to a whole number.)

Learn how to apply the Principle of Superposition to calculate the total current in a circuit with two voltage sources. Given E1 = 39V, E2 = 33V, and R = 17Ω, the total current is calculated step-by-step, with the final result of 353 mA. This problem is ideal for advanced high school students studying circuit analysis.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation