Question

assuming that voltage remains constant, what happens to the current in a filament is replaced by a longer wire? a. the current decreases. b. the current increases. c. the current alternates between high and low values. d. the current is not affected by a change in filament length.

Explanation:

Step1: Recall the formula for resistance

The resistance \(R\) of a wire is given by \(R=
ho\frac{l}{A}\), where \(
ho\) is the resistivity (constant for a given material), \(l\) is the length of the wire, and \(A\) is the cross - sectional area. When \(l\) (length) increases (assuming \(A\) and \(
ho\) are constant), \(R\) increases.

Step2: Recall Ohm's law

Ohm's law is \(I = \frac{V}{R}\), where \(V\) is voltage (constant in this case), \(I\) is current, and \(R\) is resistance. Since \(V\) is constant and \(R\) increases (from Step1), when \(R\) increases, \(I=\frac{V}{R}\) will decrease.

Answer:

A. The current decreases.