Question

For a fixed resistance, the voltage v (in volts) in an electrical circuit varies directly with the amount of current i (in amps) flowing through the circuit. If a voltage of 12 volts produces a current of 9.6 amps, write and solve a direct variation equation to find the voltage needed to produce a current of 20 amps. A voltage of __ volts would produce a current of 20 amps in the circuit.

Answer 1

Using Ohm's law (V = IR), we calculated the resistance in the circuit with the given values (12V/9.6A) and then determined the voltage needed for a 20A current, resulting in 25 volts.

Step-by-step explanation:

According to Ohm's law, the voltage v (in volts) across a resistor in an electrical circuit is directly proportional to the current i (in amps) flowing through it, as described by the equation V = IR. Given that a voltage of 12 volts produces a current of 9.6 amps, we can find the resistance R of the circuit.

Therefore, R = V/I = 12 volts / 9.6 amps = 1.25 ohms.

To find the voltage needed to produce a current of 20 amps, we use the same equation: V = IR = 20 amps * 1.25 ohms = 25 volts.

Thus, a voltage of 25 volts would produce a current of 20 amps in the circuit.