A capacitor with capacitance 2 μF is charged to 5 V. What is the energy stored in the capacitor?

A capacitor with capacitance 2 μF is charged to 5 V. What is the energy stored in the capacitor?

• A. 25 μJ
• B. 125 μJ
• C. 2.5 μJ
• D. 0.5 μJ

Answer: (A)

The energy stored in a capacitor scales with the square of the voltage and with the capacitance, given by E = (1/2) C V^2. This comes from either integrating the incremental work to charge the capacitor or using E = (1/2) QV with Q = CV. Plugging in C = 2 μF = 2×10^-6 F and V = 5 V: E = 0.5 × (2×10^-6) × (5)^2 = 1×10^-6 × 25 = 25×10^-6 J = 25 μJ. You can also check with Q = CV = (2 μF)(5 V) = 10 μC, then E = (1/2)QV = 0.5 × 10 μC × 5 V = 25 μJ, which matches.

The energy stored in a capacitor scales with the square of the voltage and with the capacitance, given by E = (1/2) C V^2. This comes from either integrating the incremental work to charge the capacitor or using E = (1/2) QV with Q = CV.

Plugging in C = 2 μF = 2×10^-6 F and V = 5 V:

E = 0.5 × (2×10^-6) × (5)^2 = 1×10^-6 × 25 = 25×10^-6 J = 25 μJ.

You can also check with Q = CV = (2 μF)(5 V) = 10 μC, then E = (1/2)QV = 0.5 × 10 μC × 5 V = 25 μJ, which matches.