Question

Which of the following terms does not represent electric power in a circuit ?

• A. \(I^2 R\)
• B. \(IR^2\)
• C. VI
• D. \(V^2/R\)

Hint:

Remember the three main formulas for electric power (\(P\)): 1. \(P = VI\) (Basic definition) 2. \(P = I^2R\) (Substitute \(V=IR\) into the first formula) 3. \(P = V^2/R\) (Substitute \(I=V/R\) into the first formula) Check the options against these:
\(I^2R\) \(\rightarrow\) Yes
\(VI\) \(\rightarrow\) Yes
\(V^2/R\) \(\rightarrow\) Yes
\(IR^2\) \(\rightarrow\) No (The R should not be squared in this way).

Answer 1

The Correct Option is B

Concept: Electric power (\(P\)) in a circuit is the rate at which electrical energy is transferred. There are several common formulas to calculate power, derived from the basic definition \(P = VI\) and Ohm's Law (\(V = IR\)). Step 1: Basic Formula for Electric Power The fundamental formula for electric power is: \[ P = VI \] where \(V\) is the voltage (potential difference) across the component and \(I\) is the current flowing through it. This matches option (3), so VI {does} represent electric power. Step 2: Derive other power formulas using Ohm's Law (\(V=IR\))
Substitute \(V = IR\) into \(P = VI\): \[ P = (IR)I = I^2R \] This matches option (1), so \(I^2R\) {does} represent electric power. This form is often used to calculate power dissipated as heat in a resistor.
Substitute \(I = V/R\) (from Ohm's Law) into \(P = VI\): \[ P = V\left(\frac{V}{R}\right) = \frac{V^2}{R} \] This matches option (4), so \(V^2/R\) {does} represent electric power. Step 3: Analyze the remaining option The options that correctly represent electric power are:
\(VI\) (Option 3)
\(I^2R\) (Option 1)
\(V^2/R\) (Option 4) The remaining option is:
(2) \(IR^2\): This expression does not correspond to any standard formula for electric power. The resistance term is squared, which is incorrect. Step 4: Conclusion The term that does not represent electric power in a circuit is \(IR^2\).