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:

$\mathbf{353 \text{ mA}}$

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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.