ur resistors are connected to a battery as shown in the ure. The current through the battery is I, the battery's R, = 2R ctromotive force (emf) is E = 8.30 V, and the resistor ues are R¡ = R, R, = 2R, R3 = 4R, and R4 = 3R. Find = voltages across each resistor. R, = R R= 3R V

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Chapter1: Units, Trigonometry. And Vectors
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**Voltage Across Resistors in a Circuit**

In this circuit diagram, four resistors are connected to a battery. The battery has an electromotive force (emf) of \( \varepsilon = 8.30 \, \text{V} \). The current through the battery is \( I \).

The diagram details the resistors with the following values:

- \( R_1 = R \)
- \( R_2 = 2R \)
- \( R_3 = 4R \)
- \( R_4 = 3R \)

The task is to find the voltage across each resistor (\( V_1, V_2, V_3, \text{and } V_4 \)).

**Diagram Explanation:**

1. **Resistor \( R_1 \)**: Located in series with the battery.
2. **Resistor \( R_2 \)**: Also in series, located above parallel arrangement.
3. **Resistor \( R_3 \)**: Positioned in parallel with \( R_4 \).
4. **Resistor \( R_4 \)**: Located in parallel with \( R_3 \) to the right of the circuit.

**Voltage Calculation:**

For each resistor, the respective voltage (\( V_i \)) can be calculated once the circuit's total resistance and current \( I \) are known, using Ohm's law \( V = IR \).

This educational content is structured to aid in understanding the calculation of voltages across each resistor in a complex circuit.
Transcribed Image Text:**Voltage Across Resistors in a Circuit** In this circuit diagram, four resistors are connected to a battery. The battery has an electromotive force (emf) of \( \varepsilon = 8.30 \, \text{V} \). The current through the battery is \( I \). The diagram details the resistors with the following values: - \( R_1 = R \) - \( R_2 = 2R \) - \( R_3 = 4R \) - \( R_4 = 3R \) The task is to find the voltage across each resistor (\( V_1, V_2, V_3, \text{and } V_4 \)). **Diagram Explanation:** 1. **Resistor \( R_1 \)**: Located in series with the battery. 2. **Resistor \( R_2 \)**: Also in series, located above parallel arrangement. 3. **Resistor \( R_3 \)**: Positioned in parallel with \( R_4 \). 4. **Resistor \( R_4 \)**: Located in parallel with \( R_3 \) to the right of the circuit. **Voltage Calculation:** For each resistor, the respective voltage (\( V_i \)) can be calculated once the circuit's total resistance and current \( I \) are known, using Ohm's law \( V = IR \). This educational content is structured to aid in understanding the calculation of voltages across each resistor in a complex circuit.
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