Chapter 34, Problem 15SP

Show that 1.00 Wb = 1.00 V • s. [Hint: Use Faraday’s Law, Eq. (32.4).]

To determine

To prove: $1.00\text{ Wb}$ is equal to $1.00\text{ V}\cdot \text{s}$

Explanation of Solution

Given data:

The value of fluxis $1.00\text{ Wb}$.

Formula used:

The magnitude of induced emf in a coil is expressed as,

$\epsilon =\left|N\frac{\Delta {\Phi }_M}{\Delta t}\right|$

Here, $N$ is the number of turns in the coil, $t$ is the time, and ${\Phi }_M$ is the magnetic flux.

Explanation:

Recall the expression for the magnitude of induced emf in the coil.

$\epsilon =\left|N\frac{\Delta {\Phi }_M}{\Delta t}\right|$

Rearrange for $\Delta {\Phi }_M$.

$\Delta {\Phi }_M=\frac{\epsilon \left(\Delta t\right)}{N}$

For 1 turn, $N=1$.

Substitute 1 for $N$

$\begin{array}{c}\Delta {\Phi }_M=\frac{\epsilon \left(\Delta t\right)}{1}\\ =\epsilon \left(\Delta t\right)\end{array}$

Write the unitsof $\Delta {\Phi }_M$, $\epsilon$, and $\Delta t$.

The unit of $\epsilon$ is volt, and $\Delta t$ is sec.

Substitute $\text{1}\text{.00 V}$ for $\epsilon$, $\text{1}\text{.00 Wb}$ for $\Delta {\Phi }_M$, and $1.00\mathrm{s}$ for $\Delta t$

$\begin{array}{c}\text{1}\text{.00 Wb}=\left(\text{1}\text{.00 V}\right)\left(1.00\mathrm{s}\right)\\ =\text{1}\text{.00 V}\cdot \text{s}\end{array}$

Conclusion:

$1.00\text{ Wb}$ is equal to $1.00\text{ V}\cdot \text{s}$.