https://file.aiquickdraw.com/mathbot/file/1728256121600iyqsovgr.jpg

To solve this circuit problem, let's analyze the setup and compute the equivalent resistance and the current through the circuit.

### Given Data:
1. Resistors:
   - \( R_1 = 21 \, \Omega \)
   - \( R_2 = 48 \, \Omega \)
   - \( R_3 = 94 \, \Omega \)

2. Potential difference between points \( A \) and \( B \): 
   - \( \Delta V = 8.5 \, \text{V} \)

### Step 1: Determine Equivalent Resistance

The configuration shows \( R_2 \) and \( R_3 \) connected in parallel, and their combination in series with \( R_1 \).

1. **Parallel Combination of \( R_2 \) and \( R_3 \):**
   \[
   \frac{1}{R_{23}} = \frac{1}{R_2} + \frac{1}{R_3}
   \]
   Substituting the values:
   \[
   \frac{1}{R_{23}} = \frac{1}{48} + \frac{1}{94}
   \]
   Calculating this gives:
   \[
   R_{23} \approx 31.88 \, \Omega
   \]

2. **Total Equivalent Resistance \( R_{\text{eq}} \):**
   Since \( R_{23} \) is in series with \( R_1 \), the total resistance is:
   \[
   R_{\text{eq}} = R_1 + R_{23} = 21 + 31.88 = 52.88 \, \Omega
   \]

### Step 2: Calculate the Current in the Circuit

Using Ohm's law:
\[
I = \frac{\Delta V}{R_{\text{eq}}} = \frac{8.5}{52.88} \approx 0.161 \, \text{A}
\]

### Step 3: Voltage Across \( R_1 \) and the Parallel Combination

1. **Voltage across \( R_1 \):**
   \[
   V_{R_1} = I \cdot R_1 = 0.161 \times 21 \approx 3.38 \, \text{V}
   \]

2. **Voltage across the parallel combination \( R_{23} \):**
   \[
   V_{R_{23}} = \Delta V - V_{R_1} = 8.5 - 3.38 \approx 5.12 \, \text{V}
   \]

### Step 4: Current through \( R_2 \) and \( R_3 \)

Using the voltage \( V_{R_{23}} \) across \( R_2 \) and \( R_3 \):
1. **Current through \( R_2 \):**
   \[
   I_{R_2} = \frac{V_{R_{23}}}{R_2} = \frac{5.12}{48} \approx 0.107 \, \text{A}
   \]

2. **Current through \( R_3 \):**
   \[
   I_{R_3} = \frac{V_{R_{23}}}{R_3} = \frac{5.12}{94} \approx 0.0545 \, \text{A}
   \]

### Summary of Results:
- Total current in the circuit: \( I \approx 0.161 \, \text{A} \)
- Voltage across \( R_1 \): \( V_{R_1} \approx 3.38 \, \text{V} \)
- Voltage across \( R_{23} \) (parallel part): \( V_{R_{23}} \approx 5.12 \, \text{V} \)
- Current through \( R_2 \): \( I_{R_2} \approx 0.107 \, \text{A} \)
- Current through \( R_3 \): \( I_{R_3} \approx 0.0545 \, \text{A} \)

Would you like further details on any specific step?

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### Related Questions:
1. How would the total current change if \( R_1 \) were increased?
2. What would happen to the equivalent resistance if \( R_2 \) and \( R_3 \) were swapped?
3. How is the power dissipated in each resistor calculated?
4. How would adding another resistor in series with \( R_1 \) affect the circuit?
5. How does parallel vs. series configuration impact voltage and current distribution?

### Tip:
For resistors in parallel, the combined resistance is always less than the smallest resistor in the group, as it provides more paths for current to flow.

Consider the three resistors R1 = 21 Ω, R2 = 48 Ω, and R3 = 94 Ω in the configuration shown in the figure. A potential difference ΔV = 8.5 V is applied between A and B. Calculate the current and the voltage distribution across the resistors.

Solve a circuit problem with resistors R1 = 21 Ω, R2 = 48 Ω, and R3 = 94 Ω connected in a mixed series-parallel configuration. Learn how to calculate the equivalent resistance, current, and voltage distribution using Ohm's Law and circuit theorems. Suitable for students in Grades 11-12 or college.

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