In the following Figure, R1=0.5 Ohm, R2=0.5 Ohm, and R3=5 Ohm. The current through R2 is 4.00 A. What is the total voltage of the battery (EMF) ? Assume the battery has no internal resistance. R1 R2 R3
In the following Figure, R1=0.5 Ohm, R2=0.5 Ohm, and R3=5 Ohm. The current through R2 is 4.00 A. What is the total voltage of the battery (EMF) ? Assume the battery has no internal resistance. R1 R2 R3
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Chapter1: Units, Trigonometry. And Vectors
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![**Problem Statement:**
In the following figure, \( R_1 = 0.5 \, \Omega \), \( R_2 = 0.5 \, \Omega \), and \( R_3 = 5 \, \Omega \). The current through \( R_2 \) is \( 4.00 \, \text{A} \). What is the total voltage of the battery (EMF)? Assume the battery has no internal resistance.
**Diagram Explanation:**
The circuit consists of three resistors \( R_1 \), \( R_2 \), and \( R_3 \). Resistors \( R_1 \) and \( R_2 \) are connected in parallel, and this parallel group is in series with \( R_3 \). The battery with EMF \( \mathcal{E} \) is connected across the entire circuit.
**Circuit Analysis:**
1. **Calculate the Voltage Across \( R_2 \):**
- Using Ohm's Law, \( V = IR \).
- The voltage across \( R_2 \) is:
\[
V_{R_2} = I_{R_2} \cdot R_2 = 4 \, \text{A} \times 0.5 \, \Omega = 2 \, \text{V}
\]
2. **Voltage Across the Parallel Combination (Since \( V_{R_1} = V_{R_2} \)):**
- Voltage across \( R_1 \) and \( R_2 \) combination: \( V_{R_1} = V_{R_2} = 2 \, \text{V} \).
3. **Determine Total Current through \( R_3 \):**
- Current through \( R_3 \) is the same total current leaving the battery.
- Total current through \( R_1 \) and \( R_2 \) in parallel is their combined currents.
4. **Use the Parallel Resistor Formula:**
\[
\frac{1}{R_{\text{parallel}}} = \frac{1}{R_1} + \frac{1}{R_2} = \frac{1}{0.5} + \frac{1}{0.5} = 4 \, \Omega^{-1}
\]
- Simpl](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb98782ef-20ba-41ff-a405-9d515999d412%2Fae2a1962-8532-4842-a4b6-efadcfb19455%2F4uu2pyu_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
In the following figure, \( R_1 = 0.5 \, \Omega \), \( R_2 = 0.5 \, \Omega \), and \( R_3 = 5 \, \Omega \). The current through \( R_2 \) is \( 4.00 \, \text{A} \). What is the total voltage of the battery (EMF)? Assume the battery has no internal resistance.
**Diagram Explanation:**
The circuit consists of three resistors \( R_1 \), \( R_2 \), and \( R_3 \). Resistors \( R_1 \) and \( R_2 \) are connected in parallel, and this parallel group is in series with \( R_3 \). The battery with EMF \( \mathcal{E} \) is connected across the entire circuit.
**Circuit Analysis:**
1. **Calculate the Voltage Across \( R_2 \):**
- Using Ohm's Law, \( V = IR \).
- The voltage across \( R_2 \) is:
\[
V_{R_2} = I_{R_2} \cdot R_2 = 4 \, \text{A} \times 0.5 \, \Omega = 2 \, \text{V}
\]
2. **Voltage Across the Parallel Combination (Since \( V_{R_1} = V_{R_2} \)):**
- Voltage across \( R_1 \) and \( R_2 \) combination: \( V_{R_1} = V_{R_2} = 2 \, \text{V} \).
3. **Determine Total Current through \( R_3 \):**
- Current through \( R_3 \) is the same total current leaving the battery.
- Total current through \( R_1 \) and \( R_2 \) in parallel is their combined currents.
4. **Use the Parallel Resistor Formula:**
\[
\frac{1}{R_{\text{parallel}}} = \frac{1}{R_1} + \frac{1}{R_2} = \frac{1}{0.5} + \frac{1}{0.5} = 4 \, \Omega^{-1}
\]
- Simpl
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