Question

The length of a 60 W, 240 Ω light bulb filament is 60 cm.

1.) Remembering that the current in the filament is proportional to the electric field, what is the current in the filament following the doubling of its length?

Express your answer using two significant figures.

2.) What is the resistance of the filament following the doubling of its length?

Express your answer using two significant figures.

Answer 1

(1)

Use ohm's law. \(R=\frac{V}{I}\)

Rearrange the above equation. \(I=\frac{V}{R}\)

When length is doubled, the resistance gets doubled since, \(R=\frac{\rho l}{A}\). \(\begin{aligned} I_{n n v} &=\frac{V}{R_{n e v}} \\ &=\frac{120 \mathrm{~V}}{2(240 \Omega)} \\ &=0.25 \mathrm{~A} \end{aligned}\)

(2)

The resistance is given by, \(R=\frac{\rho l}{A}\)

When length is doubled, the resistance will be,

\(\begin{aligned} R_{\text {new }} &=\frac{2 \rho l}{A} \\ &=2 R \\ &=2(240 \Omega) \\ &=480 \Omega \end{aligned}\)