The Principle of Superposition states that in a linear circuit with multiple independent sources, the total current through an element is the algebraic sum of the currents caused by each source acting alone, with all other sources replaced by their internal impedances.

Step 1: Understanding the Circuit Setup

We have:

• Voltage sources: $E_1 = 39V$ and $E_2 = 33V$
• Resistor: $R_1 = 17\Omega$

To find the total current through $R_1$, we consider each voltage source separately:

Step 2: Effect of $E_1$ Alone

When considering $E_1$ alone:

• Replace $E_2$ with a short circuit (since it's an ideal voltage source).
• The current caused by $E_1$ is:

$I_1 = \frac{E_1}{R_1} = \frac{39V}{17\Omega} \approx 2.2941 A$

Step 3: Effect of $E_2$ Alone

When considering $E_2$ alone:

• Replace $E_1$ with a short circuit.
• The current caused by $E_2$ is:

$I_2 = \frac{E_2}{R_1} = \frac{33V}{17\Omega} \approx 1.9412 A$

Step 4: Calculate the Total Current

Since the problem does not specify the direction of the sources explicitly, let's assume they aid each other (both currents flow in the same direction):

$I_{\text{total}} = I_1 + I_2 = 2.2941 + 1.9412 = 4.2353 A$

Step 5: Convert to Milliamperes

Since $1A = 1000mA$,

$I_{\text{total}} = 4.2353 \times 1000 = 4235.3 \text{ mA}$

Final Answer

$\boxed{4235.3 \text{ mA}}$

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Related Questions

1. How does the Principle of Superposition apply to AC circuits?
2. What happens if the voltage sources are opposing each other?
3. How would the solution change if there were additional resistors?
4. How do you handle superposition when dealing with dependent sources?
5. What is the impact of internal resistance of voltage sources in this analysis?

Tip

Always double-check source polarity when using superposition to ensure correct algebraic summation of currents or voltages.