Which expression gives the current through a resistor given voltage V across it and resistance R?

Which expression gives the current through a resistor given voltage V across it and resistance R?

• A. I = V / R
• B. I = R / V
• C. I = V R
• D. I = V^2 / R

Answer: (A)

Ohm's law tells us V = IR for a resistor. To find the current, rearrange to I = V/R. This shows current is directly proportional to voltage and inversely proportional to resistance. For example, with V = 6 V and R = 3 Ω, I = 2 A. If the voltage doubles to 12 V with the same resistor, the current doubles to 4 A. If the resistance doubles to 6 Ω while keeping 6 V, the current halves to 1 A. The other forms don’t describe current correctly: R/V would have units of ohms per volt, not amperes; V R would have units of volt-ohms, not amperes; V^2/R would have units of V^2/Ω, which isn’t current.

Ohm's law tells us V = IR for a resistor. To find the current, rearrange to I = V/R. This shows current is directly proportional to voltage and inversely proportional to resistance.

For example, with V = 6 V and R = 3 Ω, I = 2 A. If the voltage doubles to 12 V with the same resistor, the current doubles to 4 A. If the resistance doubles to 6 Ω while keeping 6 V, the current halves to 1 A.

The other forms don’t describe current correctly: R/V would have units of ohms per volt, not amperes; V R would have units of volt-ohms, not amperes; V^2/R would have units of V^2/Ω, which isn’t current.