Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 12: Problem 1708

A parallel combination of three resistors takes a current of \(7.5 \mathrm{~A}\) form a \(30 \mathrm{~V}\) supply, It the two resistors are \(10 \Omega\) and $12 \Omega$ find which is the third one? (A) \(4 \Omega\) (B) \(15 \Omega\) (C) \(12 \Omega\) (D) \(22 \Omega\)

Short Answer

Expert verified
The value of the third resistor (R3) is 15 Ω, corresponding to option (B). This is obtained by using the formula for total resistance in a parallel circuit \( \frac{1}{R_t} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} \) and values for R1, R2 and Rt. After substituting the known values, we get \( \frac{1}{R_3} = \frac{1}{4 Ω} - \frac{1}{10 Ω} - \frac{1}{12 Ω} \). Solving this equation, we find that R3 = 15 Ω.

Step by step solution

01

Write down the formula for total resistance in a parallel circuit

To find the total resistance (Rt) in a parallel circuit with three resistors (R1, R2, and R3), we use the following formula: \[\frac{1}{R_t} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}\]
02

Write down the known values

We are given the values of the first two resistors R1 and R2, and the total current (I) through the circuit. We also know the voltage (V) across the resistors. The values are: R1 = 10 Ω R2 = 12 Ω I = 7.5 A V = 30 V
03

Find the total resistance using Ohm's Law

Using Ohm's law (V = I * R), we can find the total resistance (Rt) in the circuit. Rt = V / I Plugging in the values: Rt = 30 V / 7.5 A = 4 Ω
04

Substitute the known values in the formula for total resistance

Plug in the values of Rt, R1, and R2 in the formula from Step 1: \[\frac{1}{4 \Omega} = \frac{1}{10 \Omega} + \frac{1}{12 \Omega} + \frac{1}{R_3}\]
05

Solve for the unknown resistor value (R3)

Now, we will solve this equation to find the value of R3: \[\frac{1}{R_3} = \frac{1}{4 \Omega} - \frac{1}{10 \Omega} - \frac{1}{12 \Omega}\] Find the common denominator which is 60, and solve for R3: \[\frac{1}{R_3} = \frac{15 - 6 - 5}{60} = \frac{4}{60}\] Now, flip both the numerator and denominator to find R3: \[R_3 = \frac{60}{4} = 15 \Omega\] The value of the third resistor (R3) is 15 Ω, which corresponds to option (B).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The length of a potentiometer wire is \(600 \mathrm{~cm}\) and it carries a current of \(40 \mathrm{~m} \mathrm{~A}\) for cell of emf \(2 \mathrm{~V}\) and internal resistance \(10 \Omega\), the null point is found to be at $500 \mathrm{~cm}$ on connecting a voltmeter across the cell, the balancing length is decreased by \(10 \mathrm{~cm}\) The voltmeter reading will be. (A) \(1.96 \mathrm{~V}\) (B) \(1.8 \mathrm{~V}\) (C) \(1.64 \mathrm{~V}\) (D) \(0.96 \mathrm{~V}\)

Figure, shows a network of seven resistors number 1 to 7, each equal to $1 \Omega\( connection to a \)4 \mathrm{~V}$ battery of negligible internal resistance The current I in the circuit is.... (A) \(0.5 \mathrm{~A}\) (B) \(1.5 \mathrm{~A}\) (C) \(2.0 \mathrm{~A}\) (D) \(3.5 \mathrm{~A}\)

In the circuit shown, the current sources are of negligible internal resistances. What is the potential difference between the points \(\mathrm{B}\) and \(\mathrm{A}\) ? (A) \(-4.0 \mathrm{~V}\) (B) \(4.0 \mathrm{~V}\) (C) \(-8.0 \mathrm{~V}\) (D) \(8.0 \mathrm{~V}\)

The network is made of uniform wire. The resistance of portion EL is $2 \Omega\(. Find the resistance of star between points \)F \& C .$ (A) \(0.985 \Omega\) (B) \(1.25 \Omega\) (C) \(1.946 \Omega\) (D) \(1.485 \Omega\)

In the given circuit the equivalent resistance between the points \(\mathrm{A}\) and \(\mathrm{B}\) in \(\mathrm{ohm}\) is. (A) 9 (B) \(11.6\) (C) \(14.5\) (D) \(21.2\)
See all solutions

Recommended explanations on English Textbooks

International English

Read Explanation

Synthesis Essay

Read Explanation

Lexis and Semantics Summary

Read Explanation

Syntax

Read Explanation

Single Paragraph Essay

Read Explanation

Rhetoric

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free