The Principle of Superposition states that in a linear circuit with multiple independent sources, the total current through an element is the sum of the currents caused by each source acting alone, while replacing all other voltage sources with short circuits.

Step 1: Consider E1 Alone (Set E2 = 0V by Shorting It)

• Given:
  $E_1 = 41V$, $E_2 = 20V$, $R_1 = 14\Omega$
• When E2 is replaced by a short circuit, the current due to E1 alone is:

$I_{R1}^{(E1)} = \frac{E_1}{R_1} = \frac{41V}{14\Omega} \approx 2.93A$

Step 2: Consider E2 Alone (Set E1 = 0V by Shorting It)

• When E1 is replaced by a short circuit, the current due to E2 alone is:

$I_{R1}^{(E2)} = \frac{E_2}{R_1} = \frac{20V}{14\Omega} \approx 1.43A$

Step 3: Determine the Total Current

Since both voltage sources have the same polarity, their currents add:

$I_{R1}^{\text{total}} = I_{R1}^{(E1)} + I_{R1}^{(E2)}$

$I_{R1}^{\text{total}} = 2.93A + 1.43A = 4.36A$

Step 4: Convert to Milliamperes

$I_{R1}^{\text{total}} = 4.36A \times 1000 = 4360 \text{ mA}$

Step 5: Round to the Nearest Whole Number

$\boxed{4360} \text{ mA}$

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Related Questions:

1. What is the Principle of Superposition in electrical circuits?
2. How do you determine the equivalent resistance in a series circuit?
3. What happens when two voltage sources are connected in parallel?
4. How does Kirchhoff’s Voltage Law relate to circuit analysis?
5. What is the difference between Thevenin’s and Norton’s Theorem?

Tip:

Always check the direction of current contributions when using superposition, as opposing currents should be subtracted instead of added.