### Adding a Third Radiator - Electrical Calculations When planning to add a third radiator to your garage, it is crucial to understand the electrical implications. This guide explores the scenario where the radiators can be modeled as 48 Ω resistors, focusing on the total power calculation for three such radiators. **Problem Statement:** Suppose you want to add a third radiator to your garage that is identical to the two radiators you have already installed. All three radiators can be modeled by 48 Ω resistors. Using the wiring diagram shown in Figure P2.41, calculate the total power for the three radiators. **Wiring Diagram (Figure P2.41 Explanation):** - **Source Voltage:** 240 V - The diagram shows three resistors (representing the radiators), each with a resistance of 48 Ω, connected in parallel. - The positive terminal of the 240 V power source is connected to one terminal of each resistor. - The other terminal of each resistor is connected back to the negative terminal of the power source. **Calculations:** 1. **Resistance in Parallel:** For resistors in parallel, the total or equivalent resistance, \( R_{total} \), is found using the formula: \[ \frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} \] Substituting \( R_1 = R_2 = R_3 = 48 \, \Omega \): \[ \frac{1}{R_{total}} = \frac{1}{48} + \frac{1}{48} + \frac{1}{48} = \frac{3}{48} \] Therefore: \[ R_{total} = \frac{48}{3} = 16 \, \Omega \] 2. **Total Power Calculation:** The power, \( P \), dissipated by the resistors can be calculated using the formula: \[ P = \frac{V^2}{R} \] Where \( V \) is the voltage and \( R \) is the total resistance. Substituting \( V = 240 \, \text{V} \) and \( R = 16 \, \Omega \):
### Adding a Third Radiator - Electrical Calculations When planning to add a third radiator to your garage, it is crucial to understand the electrical implications. This guide explores the scenario where the radiators can be modeled as 48 Ω resistors, focusing on the total power calculation for three such radiators. **Problem Statement:** Suppose you want to add a third radiator to your garage that is identical to the two radiators you have already installed. All three radiators can be modeled by 48 Ω resistors. Using the wiring diagram shown in Figure P2.41, calculate the total power for the three radiators. **Wiring Diagram (Figure P2.41 Explanation):** - **Source Voltage:** 240 V - The diagram shows three resistors (representing the radiators), each with a resistance of 48 Ω, connected in parallel. - The positive terminal of the 240 V power source is connected to one terminal of each resistor. - The other terminal of each resistor is connected back to the negative terminal of the power source. **Calculations:** 1. **Resistance in Parallel:** For resistors in parallel, the total or equivalent resistance, \( R_{total} \), is found using the formula: \[ \frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} \] Substituting \( R_1 = R_2 = R_3 = 48 \, \Omega \): \[ \frac{1}{R_{total}} = \frac{1}{48} + \frac{1}{48} + \frac{1}{48} = \frac{3}{48} \] Therefore: \[ R_{total} = \frac{48}{3} = 16 \, \Omega \] 2. **Total Power Calculation:** The power, \( P \), dissipated by the resistors can be calculated using the formula: \[ P = \frac{V^2}{R} \] Where \( V \) is the voltage and \( R \) is the total resistance. Substituting \( V = 240 \, \text{V} \) and \( R = 16 \, \Omega \):
Introductory Circuit Analysis (13th Edition)
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Find the total power required for the three radiators WITHOUT using PSPICE.
![### Adding a Third Radiator - Electrical Calculations
When planning to add a third radiator to your garage, it is crucial to understand the electrical implications. This guide explores the scenario where the radiators can be modeled as 48 Ω resistors, focusing on the total power calculation for three such radiators.
**Problem Statement:**
Suppose you want to add a third radiator to your garage that is identical to the two radiators you have already installed. All three radiators can be modeled by 48 Ω resistors. Using the wiring diagram shown in Figure P2.41, calculate the total power for the three radiators.
**Wiring Diagram (Figure P2.41 Explanation):**
- **Source Voltage:** 240 V
- The diagram shows three resistors (representing the radiators), each with a resistance of 48 Ω, connected in parallel.
- The positive terminal of the 240 V power source is connected to one terminal of each resistor.
- The other terminal of each resistor is connected back to the negative terminal of the power source.
**Calculations:**
1. **Resistance in Parallel:**
For resistors in parallel, the total or equivalent resistance, \( R_{total} \), is found using the formula:
\[
\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}
\]
Substituting \( R_1 = R_2 = R_3 = 48 \, \Omega \):
\[
\frac{1}{R_{total}} = \frac{1}{48} + \frac{1}{48} + \frac{1}{48} = \frac{3}{48}
\]
Therefore:
\[
R_{total} = \frac{48}{3} = 16 \, \Omega
\]
2. **Total Power Calculation:**
The power, \( P \), dissipated by the resistors can be calculated using the formula:
\[
P = \frac{V^2}{R}
\]
Where \( V \) is the voltage and \( R \) is the total resistance. Substituting \( V = 240 \, \text{V} \) and \( R = 16 \, \Omega \):](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F28d9b483-de07-43e8-9711-dcf00568269c%2Fb92787ca-a19a-4439-b0f9-9487f9d8e81a%2Fb2xq1v8_processed.png&w=3840&q=75)
Transcribed Image Text:### Adding a Third Radiator - Electrical Calculations
When planning to add a third radiator to your garage, it is crucial to understand the electrical implications. This guide explores the scenario where the radiators can be modeled as 48 Ω resistors, focusing on the total power calculation for three such radiators.
**Problem Statement:**
Suppose you want to add a third radiator to your garage that is identical to the two radiators you have already installed. All three radiators can be modeled by 48 Ω resistors. Using the wiring diagram shown in Figure P2.41, calculate the total power for the three radiators.
**Wiring Diagram (Figure P2.41 Explanation):**
- **Source Voltage:** 240 V
- The diagram shows three resistors (representing the radiators), each with a resistance of 48 Ω, connected in parallel.
- The positive terminal of the 240 V power source is connected to one terminal of each resistor.
- The other terminal of each resistor is connected back to the negative terminal of the power source.
**Calculations:**
1. **Resistance in Parallel:**
For resistors in parallel, the total or equivalent resistance, \( R_{total} \), is found using the formula:
\[
\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}
\]
Substituting \( R_1 = R_2 = R_3 = 48 \, \Omega \):
\[
\frac{1}{R_{total}} = \frac{1}{48} + \frac{1}{48} + \frac{1}{48} = \frac{3}{48}
\]
Therefore:
\[
R_{total} = \frac{48}{3} = 16 \, \Omega
\]
2. **Total Power Calculation:**
The power, \( P \), dissipated by the resistors can be calculated using the formula:
\[
P = \frac{V^2}{R}
\]
Where \( V \) is the voltage and \( R \) is the total resistance. Substituting \( V = 240 \, \text{V} \) and \( R = 16 \, \Omega \):
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