Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 12: Problem 1707

A wire \(50 \mathrm{~cm}\) long and \(1 \mathrm{~mm}^{2}\) in cross-section carries a current of \(4 \mathrm{~A}\) when connected to a \(2 \mathrm{~V}\) battery. The resistivity of the wire is: (A) \(2 \times 10^{-7} \Omega \mathrm{m}\) (B) \(5 \times 10^{-7} \Omega \mathrm{m}\) (C) \(4 \times 10^{-6} \Omega \mathrm{m}\) (D) \(1 \times 10^{-6} \Omega \mathrm{m}\)

Short Answer

Expert verified
The resistivity of the wire is \(1\times10^{-6} \Omega m\) (Option D).

Step by step solution

01

Calculate the resistance using Ohm's law

Ohm's law states that the voltage is equal to the product of current (I) and resistance (R): \[V = IR\] We are given the current (I = 4 A) and the voltage (V = 2 V). We will use Ohm's law to find the resistance (R): \[R = \frac{V}{I} = \frac{2}{4}\]
02

Find the resistance value

By solving for R, we find its value: \[R = \frac{2}{4} = 0.5 \Omega\]
03

Use the resistance formula to find resistivity

The formula for the resistance in terms of resistivity (ρ), length (L), and cross-sectional area (A) is: \[R = \frac{\rho L}{A}\] We are given the length (L = 50 cm = 0.5 m) and cross-sectional area (A = \(1 mm^2 = 1\times10^{-6} m^2\)). We will use the observed resistance (R = 0.5 Ω) and the formula to find the resistivity (ρ): \[\rho = \frac{RA}{L} = \frac{0.5 \times 1\times10^{-6}}{0.5}\]
04

Calculate the resistivity

By solving for ρ, we find its value: \[\rho = \frac{0.5 \times 1\times10^{-6}}{0.5} = 1\times10^{-6} \Omega m\] The resistivity of the wire is therefore \(1\times10^{-6} \Omega m\), which corresponds to option (D).

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 potential difference through the \(3 \Omega\) resistor shown in fig is.... (A) Zero (B) \(1 \mathrm{~V}\) (C) \(3.5 \mathrm{~V}\) (D) \(7 \mathrm{~V}\)

Assertion and reason are given in following questions each question has four options one of them is correct select it. (a) Both assertion and reason are true and the reason is correct reclamation of the assertion. (b) Both assertion and reason are true, but reason is not correct explanation of the assertion. (c) Assertion is true, but the reason is false. (d) Both, assertion and reason are false. Assertion: A series combination of cells is used when their internal resistance is much smaller than the external resistance. Reason: It follows from the relation \(\mathrm{I}=\\{(\mathrm{nE}) /(\mathrm{R}+\mathrm{nr})\\}\) Where the symbols have their standard meaning. (A) a (B) \(\mathrm{b}\) (C) \(c\) (D) \(\mathrm{d}\)

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) \(21.2\)

In each of the following questions, match column \(\mathrm{I}\) and column II and select the correct match out of the four given choicesColumn I Column II (a) The series combination of cells is for (p) More current (b) The parallel combination of cell is for (q) More voltage (c) In series combination of n cells, each of (r) \(\varepsilon\) \(\mathrm{emf}_{\mathrm{e}}\) the effective voltage is (d) In parallel combination of n cells, each of emf \(\varepsilon\) (s) ne the effective voltage is (A) \(a-p, b-q, c-r, d-s\) (B) a - q, b-p, c-r, d - s (C) \(a-q, b-p, c-s, d-r\) (D) \(a-p, b-q, c-s, d-r\)

A wire of resistor \(R\) is bent into a circular ring a circular ring of radius \(\mathrm{r}\) Equivalent resistance between two points \(\mathrm{X}\) and \(\mathrm{Y}\) on its circumference, when angle xoy is \(\alpha\), can be given by (A) $\left\\{(\mathrm{R} \alpha) /\left(4 \pi^{2}\right)\right\\}(2 \pi-\alpha)$ (B) \((\mathrm{R} / 2 \pi)(2 \pi-\alpha)\) (C) \(\mathrm{R}(2 \pi-\alpha)\) (D) \((4 \pi / \mathrm{R} \alpha)(2 \pi-\alpha)\)
See all solutions

Recommended explanations on English Textbooks

Creative Story

Read Explanation

Essay Prompts

Read Explanation

Key Concepts in Language and Linguistics

Read Explanation

International English

Read Explanation

English Grammar

Read Explanation

Lexis and Semantics

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