400 J of heat is produced in 4 seconds in a 4-ohm resistor. Calculate the potential difference (PD) across the resistor.
Answer (3)
Actually, after the information you gave, I expected you to ask for the voltage across the resistor, so I'm not quite sure what you mean by 'PD'. It could be the "Potential Difference" or the "Power Dissipation" across the resistor. Here are both answers:
Power Dissipation: Power = Energy/time = 400 joules / 4 seconds = 100 joules/second = 100 watts .
Potential Difference (voltage): Power dissipated by a resistor = (voltage)² / Resistance
100 watts = (voltage)² / 4 ohms
Multiply each side by 4 ohms:
400 watts-ohms = (voltage)²
Voltage = square root of 400 watts-ohms = 20 volts
The power dissipated in a resistor can be calculated by squaring the current passing through it and multiplying by the resistance, yielding 64 watts in this specific scenario.
The power dissipated in a resistor can be calculated using the formula P = I²R. In this case, the current through the resistor is 4 A and the resistance is 4 ohms, so the power is P = (4 A)² × 4 ohms = 64 W.
The potential difference across the 4-ohm resistor, given 400 Joules of energy produced in 4 seconds, is calculated to be 20 volts. This is derived using the power formula and the relationship between power, voltage, and resistance. Thus, the PD is confirmed to be 20 V.
;
