The figure below shows an AC source, a transformer with a turns ratio of N₁/N₂ = 2.70, a source resistor Rs, and R₂ ΔV, eeeee N₂ R₁ load resistor R₁. Ⓡ A voltmeter across the load resistor measures an rms voltage of 26.0 V when the load resistor R₁ is 48.00 and the rms source voltage is AVS = 86.0 V. (a) Determine the value of the source resistor R, (in (2). x How is the rms voltage across the secondary coil related to that of the primary? How is the power delivered to the primary related to the power delivered to the load resistor? How are the voltages across each element on the primary side related to each other? (b) What If? If the turns ratio is increased to 3.00, determine the source resistance (in 2) required to deliver the same amount of power to the load. How can you modify your work from part (a) in order to determine the source resistance required to deliver the same amount of power to the load resistor as in part (a)? Q

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The figure depicts an AC source connected to a transformer with a turns ratio of \( N_1/N_2 = 2.70 \). The circuit also includes a source resistor \( R_S \) and a load resistor \( R_L \).

### Description of Circuit Elements:
1. **AC Source (\( \Delta V_S \))**: Provides an rms voltage of 86.0 V.
2. **Transformer**: 
   - Primary coil (\( N_1 \))
   - Secondary coil (\( N_2 \))
   - Turns ratio of \( N_1/N_2 = 2.70 \)

3. **Source Resistor (\( R_S \))**: Value to be determined.
4. **Load Resistor (\( R_L \))**: Has a resistance of 48.0 \(\Omega\).

### Measurements:
- The voltmeter across the load resistor measures an rms voltage of 26.0 V.

### Tasks:

#### (a) Determine the Value of the Source Resistor \( R_S \) (in \(\Omega\)):
- Consider the relationship between rms voltages across the primary and secondary coils.
- Analyze how power is transferred from the primary to the load resistor.
  
**Guidance**: Reflect on the voltage relationship in each part of the circuit and the power delivery relative to each element.

#### (b) Analyze the Case When the Turns Ratio is Increased to 3.00:
- Calculate the \( R_S \) needed to deliver the same power to the load as in part (a).

**Guidance**: Adjust your approach from part (a) to account for the change in the turns ratio and its effect on source resistance and power delivery.

### General Tips:
- Understand the role of the transformer in adjusting voltage and current levels.
- Use Kirchhoff's laws and power equations to establish relationships between circuit parameters.
- Consider the efficiency and power conservation principles in transformers while solving the problems.
Transcribed Image Text:The figure depicts an AC source connected to a transformer with a turns ratio of \( N_1/N_2 = 2.70 \). The circuit also includes a source resistor \( R_S \) and a load resistor \( R_L \). ### Description of Circuit Elements: 1. **AC Source (\( \Delta V_S \))**: Provides an rms voltage of 86.0 V. 2. **Transformer**: - Primary coil (\( N_1 \)) - Secondary coil (\( N_2 \)) - Turns ratio of \( N_1/N_2 = 2.70 \) 3. **Source Resistor (\( R_S \))**: Value to be determined. 4. **Load Resistor (\( R_L \))**: Has a resistance of 48.0 \(\Omega\). ### Measurements: - The voltmeter across the load resistor measures an rms voltage of 26.0 V. ### Tasks: #### (a) Determine the Value of the Source Resistor \( R_S \) (in \(\Omega\)): - Consider the relationship between rms voltages across the primary and secondary coils. - Analyze how power is transferred from the primary to the load resistor. **Guidance**: Reflect on the voltage relationship in each part of the circuit and the power delivery relative to each element. #### (b) Analyze the Case When the Turns Ratio is Increased to 3.00: - Calculate the \( R_S \) needed to deliver the same power to the load as in part (a). **Guidance**: Adjust your approach from part (a) to account for the change in the turns ratio and its effect on source resistance and power delivery. ### General Tips: - Understand the role of the transformer in adjusting voltage and current levels. - Use Kirchhoff's laws and power equations to establish relationships between circuit parameters. - Consider the efficiency and power conservation principles in transformers while solving the problems.
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