Problem

A resistor of $50 \, \Omega$ has a potential difference of $100 \, \mathrm{V}$ DC across it for $1 \, \mathrm{hour}$.
(a) Calculate the power consumed.
(b) Calculate the total energy consumed.

Data

• Resistance: $R = 50 \, \Omega$
• Potential Difference: $V = 100 \, \mathrm{V}$
• Time: $\Delta t = 1 \, \mathrm{hour} = 3600 \, \mathrm{s}$

Prerequisite Concepts

1. Power Formula:
   $P = \frac{V^2}{R}$
2. Energy Formula:
   $E = P \cdot t$

Solution

(a) Power:

$$P = \frac{V^2}{R} = \frac{(100)^2}{50} = 200 \, \mathrm{W}.$$

(b) Energy:

$$E = P \cdot t = 200 \cdot 3600 = 0.72 \, \mathrm{MJ}.$$

Answer

• Power: $P = 200 \, \mathrm{W}$
• Energy: $E = 0.72 \, \mathrm{MJ}$

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