Ohm's Law and Electrical Power Relationships

Steps:

• Recall Ohm's law: V = IR, so I = V/R and R = V/I.
• Power dissipated: P = VI, so I = P/V and P = V²/R (substituting I = V/R).
• Work done: W = VQ (energy transferred by p.d. to charge), so Q = W/V.
• Check each option against these formulas to identify the invalid one.

Why D is correct:

• R = V/P rearranges P = VI to R = V/(VI) = 1/I, which ignores R's dependence on V and I via Ohm's law.

Why the others are wrong:

• A is valid: From P = VI, I = P/V.
• B is valid: From W = VQ, Q = W/V.
• C is valid: From P = V²/R (substituting I = V/R into P = VI).

Final answer: D