Question

4.1.2 quiz: electricity
question 3 of 10
a student is planning to make changes to a circuit. which change will increase the current?
a. replace the wire with one that is thicker.
b. add an electric bell to the circuit.
c. replace the wire with one that is thinner.
d. replace the existing battery with a smaller battery.

Explanation:

Step1: Recall Ohm's Law

Ohm's Law is \(I = \frac{V}{R}\), where \(I\) is current, \(V\) is voltage, and \(R\) is resistance. To increase \(I\), we need to decrease \(R\) (assuming \(V\) is constant) or increase \(V\) (assuming \(R\) is constant).

Step2: Analyze resistance formula

The resistance formula is \(R=
ho\frac{l}{A}\), where \(
ho\) is resistivity (property of material), \(l\) is length, and \(A\) is cross - sectional area. A thicker wire has a larger \(A\). From \(R=
ho\frac{l}{A}\), when \(A\) increases, \(R\) decreases.

Step3: Analyze each option

• Option A: Thicker wire (\(A\) increases). Using \(R =

ho\frac{l}{A}\), \(R\) decreases. Then using \(I=\frac{V}{R}\) (assuming \(V\) from battery is constant), \(I\) increases.

• Option B: Adding an electric bell (a resistor) increases the total resistance \(R\). Using \(I=\frac{V}{R}\), \(I\) decreases.
• Option C: Thinner wire (\(A\) decreases). Using \(R=

ho\frac{l}{A}\), \(R\) increases. Using \(I = \frac{V}{R}\), \(I\) decreases.

• Option D: Smaller battery likely has lower voltage \(V\). Using \(I=\frac{V}{R}\) (assuming \(R\) is constant), \(I\) decreases.

Answer:

A. Replace the wire with one that is thicker.