Question

1. the electric current i, in amperes, in a circuit varies directly as the voltage v. when 18 volts are applied, the current is 4 amperes. what is the current when 24 volts are applied?

Explanation:

Step1: Define direct variation

For direct variation, \( I = kV \), where \( k \) is the constant of proportionality.

Step2: Find \( k \) using given values

When \( V = 18 \) volts, \( I = 4 \) amperes. Substitute into \( I = kV \):
\( 4 = k \times 18 \)
Solve for \( k \): \( k = \frac{4}{18} = \frac{2}{9} \)

Step3: Find \( I \) for \( V = 24 \) volts

Use \( I = kV \) with \( k = \frac{2}{9} \) and \( V = 24 \):
\( I = \frac{2}{9} \times 24 = \frac{48}{9} = \frac{16}{3} \approx 5.33 \) (or keep as a fraction)

Answer:

The current is \(\frac{16}{3}\) amperes (or approximately \(5.33\) amperes).