Final answer:
The resistance of the resistor through which 500 joules of energy is used to move 100 C of charge is 50 ohms. By using the formula W = QV and rearranging it as V = W/Q, we get the voltage, and then applying Ohm's law (V = IR), we can solve for the resistance, resulting in 50 ohms.
Step-by-step explanation:
To find the resistance of the resistor given that 500 joules of energy are used to move 100 C of charge through it, we can use the relationship between energy (W), charge (Q), and voltage (V) given by W = QV. Then, using Ohm's law, V = IR (where I is current and R is resistance), we can find the resistance. By substituting the voltage from the first equation (V = W/Q) into Ohm's law, we have I = W/(QR).
To find the current, I, we need to know the voltage. With the given energy and charge, the voltage can be calculated as V = W/Q = 500 J / 100 C = 5 V. Now we can find the current by rearranging Ohm's law: I = V/R. But the current is also the charge per unit time, and since no time is specified, we can assume the charge moved through the resistor at once, so I = Q in amps, which is 100 C = 100 A. Therefore, R = V/I = 5 V / 100 A = 0.05 Ω. To convert to ohms, multiply by 1000 (since 1 A = 1 C/s), giving R = 50 Ω.