Question

how does the current in a resistor change if the voltage across the resistor is decreased by a factor of 4?
a. it decreases by a factor of 2.
b. it decreases by a factor of 4.
c. it increases by a factor of 2.
d. it increases by a factor of 4.

Explanation:

Step1: Recall Ohm's Law

Ohm's Law is given by \(I=\frac{V}{R}\), where \(I\) is the current, \(V\) is the voltage, and \(R\) is the resistance. Assume the resistance \(R\) is constant (since the problem is about the effect of voltage change on current for a given resistor).

Step2: Analyze the change in current

Let the initial voltage be \(V_1\) and the initial current be \(I_1=\frac{V_1}{R}\). The new voltage \(V_2 = \frac{V_1}{4}\). Then the new current \(I_2=\frac{V_2}{R}=\frac{\frac{V_1}{4}}{R}\). Substitute \(I_1=\frac{V_1}{R}\) into the equation for \(I_2\), we get \(I_2=\frac{I_1}{4}\).

Answer:

B. It decreases by a factor of 4.