https://file.aiquickdraw.com/mathbot/file/17270803381887bjtx24k.jpg

The circuit in the image shows a combination of resistors and a 24V voltage source (\(V_s = 24V\)). The resistors are labeled:

- \( R_1 = 6 \Omega \)
- \( R_2 = 8 \Omega \)
- \( R_3 = 4 \Omega \)
- \( R_4 = 12 \Omega \)

It appears to be a bridge circuit, but it is drawn in a slightly non-standard form. To determine the current \( I \) through the circuit, we can follow these steps:

### Steps to Solve for Current \( I \):

1. **Simplify the circuit**: We can combine resistors where possible.
   - \( R_2 \) and \( R_3 \) form a series combination because they are connected end-to-end.
     \[
     R_{23} = R_2 + R_3 = 8 \Omega + 4 \Omega = 12 \Omega
     \]
   - Now, \( R_{23} \) and \( R_4 \) are in parallel, since they are connected across the same nodes.
     \[
     \frac{1}{R_{eq}} = \frac{1}{R_{23}} + \frac{1}{R_4} = \frac{1}{12 \Omega} + \frac{1}{12 \Omega}
     \]
     Solving this, we get:
     \[
     R_{eq} = 6 \Omega
     \]

2. **Total resistance in the circuit**: Now that we have reduced the parallel part of the circuit, this resistance \( R_{eq} = 6 \Omega \) is in series with \( R_1 \). Therefore, the total resistance \( R_{total} \) is:
   \[
   R_{total} = R_1 + R_{eq} = 6 \Omega + 6 \Omega = 12 \Omega
   \]

3. **Apply Ohm’s Law**: Now, using Ohm's Law, we can find the current \( I \):
   \[
   I = \frac{V_s}{R_{total}} = \frac{24V}{12 \Omega} = 2A
   \]

Thus, the current \( I \) in the circuit is **2A**.

Would you like further details on the process or have any other questions?

### Related Questions:
1. How do we calculate the voltage drop across each resistor?
2. What is the power dissipated by each resistor in the circuit?
3. How would the current change if \( R_4 \) were increased to 20 \( \Omega \)?
4. How do we find the equivalent resistance in a more complex bridge circuit?
5. What is the significance of a balanced bridge circuit in practical applications?

### Tip:
Always look for resistors in series or parallel to simplify complex circuits before applying Ohm's law for easier calculation.

Determine the current I in the given circuit with a 24V source and resistors R1 = 6Ω, R2 = 8Ω, R3 = 4Ω, and R4 = 12Ω.

Learn how to calculate the total current in a series-parallel circuit with resistors R1 = 6Ω, R2 = 8Ω, R3 = 4Ω, and R4 = 12Ω, using Ohm's Law and series-parallel combinations. Suitable for high school students studying circuit analysis.

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