A 4.0-2 resistor is connected to a 12-2 resistor and this combination is connected to an ideal dc power supply with voltage V = 12 volts as shown in the figure. What is the value of current in the 12- resistor? O 1 A O 3 A O 12 A O 15 A 4 A 4.00 www www 12 Ω
A 4.0-2 resistor is connected to a 12-2 resistor and this combination is connected to an ideal dc power supply with voltage V = 12 volts as shown in the figure. What is the value of current in the 12- resistor? O 1 A O 3 A O 12 A O 15 A 4 A 4.00 www www 12 Ω
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Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
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![**Problem Statement:**
A 4.0-Ω resistor is connected to a 12-Ω resistor and this combination is connected to an ideal DC power supply with voltage \( V = 12 \) volts as shown in the figure. What is the value of current in the 12-Ω resistor?
**Diagram Explanation:**
The diagram shows a circuit with a 4.0-Ω resistor and a 12-Ω resistor connected in parallel to each other. This parallel combination is connected to a DC power supply of 12 volts. Current \( I \) flows from the voltage source, splitting at the junction before the resistors.
**Solution Options:**
- ○ 1 A
- ○ 3 A
- ○ 12 A
- ○ 15 A
- ○ 4 A
**Analysis:**
To find the current through the 12-Ω resistor, we can use the formula for current in a parallel circuit and Ohm's Law (\( V = IR \)).
1. Calculate the total resistance in parallel:
\[
\frac{1}{R_{\text{total}}} = \frac{1}{4} + \frac{1}{12}
\]
Solving for \( R_{\text{total}} \):
\[
R_{\text{total}} = \frac{1}{\left( \frac{1}{4} + \frac{1}{12} \right)} = \frac{1}{\frac{1+3}{12}} = \frac{12}{4} = 3 \, \text{Ω}
\]
2. Calculate the total current from the power supply:
\[
I_{\text{total}} = \frac{V}{R_{\text{total}}} = \frac{12 \, \text{V}}{3 \, \text{Ω}} = 4 \, \text{A}
\]
3. Current through the 12-Ω resistor:
Using the current divider rule:
\[
I_{12 \, \text{Ω}} = I_{\text{total}} \times \frac{R_{\text{other}}}{R_{\text{total}}} = 4 \, \text{A} \times \frac{4}{3}
\]
\[
I_{12 \, \text{Ω}} = \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4889a1b2-cd02-493f-a3b5-7c3cbfe1f622%2Fd1350be1-ba94-4263-8fd8-4d6a03fde0df%2Fv15hbiy_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A 4.0-Ω resistor is connected to a 12-Ω resistor and this combination is connected to an ideal DC power supply with voltage \( V = 12 \) volts as shown in the figure. What is the value of current in the 12-Ω resistor?
**Diagram Explanation:**
The diagram shows a circuit with a 4.0-Ω resistor and a 12-Ω resistor connected in parallel to each other. This parallel combination is connected to a DC power supply of 12 volts. Current \( I \) flows from the voltage source, splitting at the junction before the resistors.
**Solution Options:**
- ○ 1 A
- ○ 3 A
- ○ 12 A
- ○ 15 A
- ○ 4 A
**Analysis:**
To find the current through the 12-Ω resistor, we can use the formula for current in a parallel circuit and Ohm's Law (\( V = IR \)).
1. Calculate the total resistance in parallel:
\[
\frac{1}{R_{\text{total}}} = \frac{1}{4} + \frac{1}{12}
\]
Solving for \( R_{\text{total}} \):
\[
R_{\text{total}} = \frac{1}{\left( \frac{1}{4} + \frac{1}{12} \right)} = \frac{1}{\frac{1+3}{12}} = \frac{12}{4} = 3 \, \text{Ω}
\]
2. Calculate the total current from the power supply:
\[
I_{\text{total}} = \frac{V}{R_{\text{total}}} = \frac{12 \, \text{V}}{3 \, \text{Ω}} = 4 \, \text{A}
\]
3. Current through the 12-Ω resistor:
Using the current divider rule:
\[
I_{12 \, \text{Ω}} = I_{\text{total}} \times \frac{R_{\text{other}}}{R_{\text{total}}} = 4 \, \text{A} \times \frac{4}{3}
\]
\[
I_{12 \, \text{Ω}} = \
Expert Solution
Step 1
Given:-
Resistance of the resistors are
Voltage of the supply source is
Required:-
Current through the resistor.
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