Chapter 34, Problem 49A

(a)

To determine

To Explain: The new resistance when the length of the copper wire is halved.

Explanation of Solution

Introduction:

Resistance is a property of element which is introduced in a circuit or the material of the conducting wire. When current is passed through a conducting wire, it heats up.

The resistance of a wire depends on its length. If the length of the wire is halved, the value of resistance would also be halved.

Conclusion:

Thus, new resistance would be 5 ohms.

(b)

To determine

To Explain: The new resistance when the length of the copper wire is halved.

Explanation of Solution

Introduction:

Resistance is a property of element which is introduced in a circuit or the material of the conducting wire. When current is passed through a conducting wire, it heats up.

Resistance of a wire depends on its length $\left(l\right)$ , thickness $\left(d\right)$ and resistivity $\left(\rho \right)$ .

  $R=\frac{\rho l}{\pi d^2}$

If the wire is doubled such that the length is halved and cross-sectional area is doubled, then the resistance of the wire would be one-fourth of the former value.

Conclusion:

Thus, new resistance would be $2.5$ ohms.