GSO001 Problem 4
Problem Statement
Heat Generated by a Resistive Heating Element
Problem Statement
In an electric circuit, a heating element with resistance R is connected. When a voltage V is applied to this element, a constant current I flows. First, find the electric power P consumed by the heating element. Then find the heat (Joule heat) Q generated by the element when the current flows for time t.
Constraints
- Voltage V=24 V
- Current I=1.5 A
- Time t=300 s
Input Format
Find the value of heat Q generated and give the answer as a positive integer.
Solution
This problem is a two-step calculation: first applying the definition of electric power, then the definition of heat.
1. Step 1: Computing Power P
The power P consumed by the heating element is the product of voltage V and current I:
P=V×ISubstituting numerical values:
P=24 V×1.5 A=36 W2. Step 2: Computing Heat Q
The heat Q generated by the heating element is the product of power P and the time t the current flows:
Q=P×tSubstituting:
Q=36 W×300 s=10800 JTherefore, the heat generated is 10800.
Answer: 10800