Answered: If the three resistors 47k ohm, 220k…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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Question

If the three resistors 47k ohm, 220k ohm and 3.3k ohm are in parallel circuit and each rated at 0.5 W, what is the maximum total current that the network can handle without overheating any resistor?

Expert Solution

Step 1

The three resistors connected in parallel is shown below:

The total current will be the sum of the current across each resistor(branches), the expression is shown below:

$I = i_{1} + i_{2} + i_{3} . . . . . . . . . . . . . . . . . . (1)$

Since the maximum power that can be dissipated across each resistor is 0.5 W, the current across each resistor is calculated by the expression of the power.

The maximum current across the first resistor is,

$p_{1} (m a x) = {i_{1}}^{2} R_{1} R_{1} = 47 k Ω p_{1} (m a x) = 0.5 W 0.5 = {i_{1}}^{2} \times 47 \times 10^{3} {i_{1}}^{2} = \frac{0.5}{47 \times 10^{3}} {i_{1}}^{2} = 1.06383 \times 10^{- 5} i_{1} = 3.2616 \times 10^{- 3} A$