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calculate the current through each resistior

The image displays an electrical circuit with two voltage sources \( E_1 = 8V \) and \( E_2 = 24V \), along with three resistors: \( R_1 = 2\Omega \), \( R_2 = 1\Omega \), and \( R_3 = 4\Omega \).

This is a parallel circuit, with the following components:

- \( R_1 \) and \( R_2 \) are directly connected to their respective voltage sources \( E_1 \) and \( E_2 \).
- \( R_3 \) shares a node between both branches.

To find the current through each resistor, we can apply **Ohm's Law**:

\[
I = \frac{V}{R}
\]

We calculate the current through each resistor as follows:

### 1. **Current through \( R_1 \)**:
This resistor is in the branch with the 8V source:

\[
I_1 = \frac{E_1}{R_1} = \frac{8V}{2\Omega} = 4A
\]

### 2. **Current through \( R_2 \)**:
This resistor is in the branch with the 24V source:

\[
I_2 = \frac{E_2}{R_2} = \frac{24V}{1\Omega} = 24A
\]

### 3. **Current through \( R_3 \)**:
\( R_3 \) is shared between the two sources. To find the current through \( R_3 \), we need to analyze the potential difference across it, considering the voltages at the junction between the two sources.

If we assume the potential difference across \( R_3 \) is due to the difference between the two voltages, we get:

\[
\Delta V_{R_3} = E_2 - E_1 = 24V - 8V = 16V
\]

Then the current through \( R_3 \) is:

\[
I_3 = \frac{\Delta V_{R_3}}{R_3} = \frac{16V}{4\Omega} = 4A
\]

### Summary of Currents:
- \( I_1 = 4A \)
- \( I_2 = 24A \)
- \( I_3 = 

Calculate the current through each resistor in the given circuit with E1=8V, E2=24V, R1=2Ω, R2=1Ω, and R3=4Ω.

Learn how to calculate the current through each resistor in a circuit with two voltage sources (8V and 24V) and three resistors (2Ω, 1Ω, and 4Ω) using Ohm's Law. The solution involves analyzing the potential difference across shared components and applying key electrical concepts.

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