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nd the total resistance of the combination of resistors shown in the figure below. Answer is in µΩ. (R1 = 18.0 µΩ, R2 = 5.50 µΩ, and R3 = 0.300 µΩ.)

nd the total resistance of the combination of resistors shown in the figure below. Answer is in µΩ. (R1 = 18.0 µΩ, R2 = 5.50 µΩ, and R3 = 0.300 µΩ.)

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Find the total resistance of the combination of resistors shown in the figure below. Answer is in µΩ.

(R1 = 18.0 µΩ, R2 = 5.50 µΩ, and R3 = 0.300 µΩ.)
 
 
 
The image illustrates a resistor circuit diagram featuring three resistors. Resistor \( R_1 \) and Resistor \( R_2 \) are positioned in parallel with each other, forming a parallel connection. This parallel configuration is then followed by Resistor \( R_3 \), which is in series with the parallel combination of \( R_1 \) and \( R_2 \). ### Detailed Explanation: - **Parallel Resistors \( R_1 \) and \( R_2 \):** - The two resistors are connected such that their ends are connected together, allowing current to split and flow through them simultaneously. This configuration effectively reduces the total resistance of the circuit in the parallel section. - **Series Resistor \( R_3 \):** - Following the parallel section, Resistor \( R_3 \) is connected in series. This means that the current flowing from the parallel part passes entirely through \( R_3 \) before continuing on through the circuit. In a series connection, resistors are additively combined in terms of their resistance. ### Calculation: - **Equivalent Resistance for Parallel Resistors (\( R_1 \) and \( R_2 \)):** \[ \frac{1}{R_{\text{parallel}}} = \frac{1}{R_1} + \frac{1}{R_2} \] Thus, the total equivalent resistance of \( R_1 \) and \( R_2 \) in parallel is given by: \[ R_{\text{parallel}} = \frac{R_1 \cdot R_2}{R_1 + R_2} \] - **Total Resistance of the Circuit:** \[ R_{\text{total}} = R_{\text{parallel}} + R_3 \] This calculates the total resistance of the circuit, taking into account both the parallel and series components.
Transcribed Image Text:The image illustrates a resistor circuit diagram featuring three resistors. Resistor \( R_1 \) and Resistor \( R_2 \) are positioned in parallel with each other, forming a parallel connection. This parallel configuration is then followed by Resistor \( R_3 \), which is in series with the parallel combination of \( R_1 \) and \( R_2 \). ### Detailed Explanation: - **Parallel Resistors \( R_1 \) and \( R_2 \):** - The two resistors are connected such that their ends are connected together, allowing current to split and flow through them simultaneously. This configuration effectively reduces the total resistance of the circuit in the parallel section. - **Series Resistor \( R_3 \):** - Following the parallel section, Resistor \( R_3 \) is connected in series. This means that the current flowing from the parallel part passes entirely through \( R_3 \) before continuing on through the circuit. In a series connection, resistors are additively combined in terms of their resistance. ### Calculation: - **Equivalent Resistance for Parallel Resistors (\( R_1 \) and \( R_2 \)):** \[ \frac{1}{R_{\text{parallel}}} = \frac{1}{R_1} + \frac{1}{R_2} \] Thus, the total equivalent resistance of \( R_1 \) and \( R_2 \) in parallel is given by: \[ R_{\text{parallel}} = \frac{R_1 \cdot R_2}{R_1 + R_2} \] - **Total Resistance of the Circuit:** \[ R_{\text{total}} = R_{\text{parallel}} + R_3 \] This calculates the total resistance of the circuit, taking into account both the parallel and series components.
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