Three resistors, R1=3.00 ohms, R2+ 4.00 ohms, R3 =4.00 ohms, are connected in parallel. With what single equivalent resistance Req could the parallel combination be replaced? if the parallel combination is connected to a 12.0V battery, what is the currnt in each resistor?

Three resistors, R1=3.00 ohms, R2+ 4.00 ohms, R3 =4.00 ohms, are connected in parallel. With what single equivalent resistance Req could the parallel combination be replaced? if the parallel combination is connected to a 12.0V battery, what is the currnt in each resistor?

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 19PQ

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Question

Expert Solution

Step 1

Given:

Three resistors arranged in parallel where,

$R_{1} = 3 Ω$

$R_{2} = 4 Ω$

$R_{3} = 4 Ω$

Battery voltage, $V = 12 V$

Step 2

Equivalent resistance that could replaced this parallel combination of resistors is calculated as:

$\frac{1}{R_{e q}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}} \Rightarrow \frac{1}{R_{e q}} = \frac{1}{3} + \frac{1}{4} + \frac{1}{4} \Rightarrow \frac{1}{R_{e q}} = \frac{4 + 3 + 3}{12} = \frac{10}{12} \Rightarrow R_{e q} = 1.2 Ω$

Hence, total resistance is $1.2 Ω$ .

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