In the circuit shown below, determine the current in the circuit. How much power is dissipated by each resistor in the figure? R₁ = 120 9.0 V R₂= = 15 Ω wwwwww
In the circuit shown below, determine the current in the circuit. How much power is dissipated by each resistor in the figure? R₁ = 120 9.0 V R₂= = 15 Ω wwwwww
Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Katz, Debora M.
Chapter29: Direct Current (dc) Circuits
Section: Chapter Questions
Problem 21PQ
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Question
![**Determine Current and Power in Series Circuit**
**Problem Overview:**
In the circuit shown below, determine the current in the circuit. How much power is dissipated by each resistor in the figure?
**Circuit Diagram:**
The circuit consists of a series connection with the following components:
- A voltage source of 9.0 volts (V).
- Two resistors:
- \( R_1 \) with a resistance of 12 ohms (Ω).
- \( R_2 \) with a resistance of 15 ohms (Ω).
**Analysis:**
1. **Total Resistance in the Circuit:**
Since the resistors are in series, the total resistance \( R_t \) is the sum of the resistances:
\[
R_t = R_1 + R_2 = 12 \, \Omega + 15 \, \Omega = 27 \, \Omega
\]
2. **Current in the Circuit:**
Using Ohm's Law to determine the current \( I \) in the circuit:
\[
I = \frac{V}{R_t} = \frac{9.0 \, \text{V}}{27 \, \Omega} = 0.33 \, \text{A} \, (\text{or } \frac{1}{3} \, \text{A})
\]
3. **Power Dissipated by Each Resistor:**
- For \( R_1 \):
\[
P_1 = I^2 \times R_1 = (0.33 \, \text{A})^2 \times 12 \, \Omega = 0.11 \, \text{W}
\]
- For \( R_2 \):
\[
P_2 = I^2 \times R_2 = (0.33 \, \text{A})^2 \times 15 \, \Omega = 0.165 \, \text{W}
\]
**Conclusion:**
The current in the circuit is 0.33 A. The power dissipated by resistor \( R_1 \) is 0.11 W, and the power dissipated by resistor \( R_2 \) is 0.165 W.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4a6e4794-5644-431d-9e96-b37fbaf0b60a%2F13ea38f3-ca6d-45f1-a1eb-dcb3f1302ad7%2Fqrxuswt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Determine Current and Power in Series Circuit**
**Problem Overview:**
In the circuit shown below, determine the current in the circuit. How much power is dissipated by each resistor in the figure?
**Circuit Diagram:**
The circuit consists of a series connection with the following components:
- A voltage source of 9.0 volts (V).
- Two resistors:
- \( R_1 \) with a resistance of 12 ohms (Ω).
- \( R_2 \) with a resistance of 15 ohms (Ω).
**Analysis:**
1. **Total Resistance in the Circuit:**
Since the resistors are in series, the total resistance \( R_t \) is the sum of the resistances:
\[
R_t = R_1 + R_2 = 12 \, \Omega + 15 \, \Omega = 27 \, \Omega
\]
2. **Current in the Circuit:**
Using Ohm's Law to determine the current \( I \) in the circuit:
\[
I = \frac{V}{R_t} = \frac{9.0 \, \text{V}}{27 \, \Omega} = 0.33 \, \text{A} \, (\text{or } \frac{1}{3} \, \text{A})
\]
3. **Power Dissipated by Each Resistor:**
- For \( R_1 \):
\[
P_1 = I^2 \times R_1 = (0.33 \, \text{A})^2 \times 12 \, \Omega = 0.11 \, \text{W}
\]
- For \( R_2 \):
\[
P_2 = I^2 \times R_2 = (0.33 \, \text{A})^2 \times 15 \, \Omega = 0.165 \, \text{W}
\]
**Conclusion:**
The current in the circuit is 0.33 A. The power dissipated by resistor \( R_1 \) is 0.11 W, and the power dissipated by resistor \( R_2 \) is 0.165 W.
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