The circuit below has three parallel resistors R₁= 4K, R₂=6 KQ and R3= 12 KM, and a supply voltage of 24 Volts. What will be the total resistor value? 22.0 ΚΩ 2.0ΚΩ 1.4ΚΩ 32.0 ΚΩ OLUSUD VSupply R₁ R₂ R3
The circuit below has three parallel resistors R₁= 4K, R₂=6 KQ and R3= 12 KM, and a supply voltage of 24 Volts. What will be the total resistor value? 22.0 ΚΩ 2.0ΚΩ 1.4ΚΩ 32.0 ΚΩ OLUSUD VSupply R₁ R₂ R3
Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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![### Understanding Parallel Resistor Circuits
The circuit diagram illustrates a setup with three parallel resistors:
- \( R_1 = 4 \, \text{K}\Omega \)
- \( R_2 = 6 \, \text{K}\Omega \)
- \( R_3 = 12 \, \text{K}\Omega \)
These resistors are connected to a voltage supply of 24 Volts. The question posed is: **What will be the total resistor value?**
In parallel circuits, the total resistance (\( R_t \)) can be found using the formula:
\[
\frac{1}{R_t} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}
\]
#### Options for Total Resistance
1. \( 22.0 \, \text{K}\Omega \)
2. \( 2.0 \, \text{K}\Omega \)
3. \( 1.4 \, \text{K}\Omega \)
4. \( 32.0 \, \text{K}\Omega \)
To solve for the total resistance, the formula allows us to calculate the multiplicative inverse of the sum of all individual inverse resistances. The correct choice is the one that fits this calculated total.
#### Diagram Explanation
The circuit diagram shows three resistors arranged in parallel, connected to an ideal voltage source labeled as \( V_{\text{Supply}} \). Lines represent wired connections between the components, indicating the parallel configuration where each resistor has two terminals that ensure equal voltage across all resistors.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1b551779-a94f-4658-8ab9-cb1269496a60%2F3cd9b01e-438d-4f4e-8428-9afe628a10a6%2Fju8jmv_processed.png&w=3840&q=75)
Transcribed Image Text:### Understanding Parallel Resistor Circuits
The circuit diagram illustrates a setup with three parallel resistors:
- \( R_1 = 4 \, \text{K}\Omega \)
- \( R_2 = 6 \, \text{K}\Omega \)
- \( R_3 = 12 \, \text{K}\Omega \)
These resistors are connected to a voltage supply of 24 Volts. The question posed is: **What will be the total resistor value?**
In parallel circuits, the total resistance (\( R_t \)) can be found using the formula:
\[
\frac{1}{R_t} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}
\]
#### Options for Total Resistance
1. \( 22.0 \, \text{K}\Omega \)
2. \( 2.0 \, \text{K}\Omega \)
3. \( 1.4 \, \text{K}\Omega \)
4. \( 32.0 \, \text{K}\Omega \)
To solve for the total resistance, the formula allows us to calculate the multiplicative inverse of the sum of all individual inverse resistances. The correct choice is the one that fits this calculated total.
#### Diagram Explanation
The circuit diagram shows three resistors arranged in parallel, connected to an ideal voltage source labeled as \( V_{\text{Supply}} \). Lines represent wired connections between the components, indicating the parallel configuration where each resistor has two terminals that ensure equal voltage across all resistors.
Expert Solution
Step 1
The sum of the individual resistances in a series circuit determines the total resistance. As additional components are added, there are more channels for the current to travel through, lowering the net resistance of the parallel circuit. The current in each resistor in a series circuit is the same because the output current from the first resistor flows into the input of the second resistor. In a parallel circuit, the leads on the resistors' one side and their other side are both linked.
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