http://www.ck12.org Chapter 17. CircuitsJoule HeatingThe equationP=IV is true for any electrical device. We can therefore use this equation to compute the power
dissipated through a resistor.
The rate at which the energy (power) is dissipated through a resistor is referred to asJoule heating.
Using the equationV=IR, the Joule heating for a resistor isP=IV=I(IR) =I^2 R, assuming the resistance is
constant, orP=IV=VRV=V
2
R, assuming the resistance is constant.
The rate of energy transfer can be so high, that unless care is taken, a resistor will not be able to transfer the heat
quickly enough to the air before overheating and burning out. Installing a resistor with a low power rating when one
with a higher rating should have been used can ruin an expensive piece of equipment.
You can easily see the effect of Joule heating with an incandescent light bulb. It has a thin tungsten filament which
heats ups very quickly. You don’t want to touch an incandescent bulb even if it’s only been turned on for a minute.
Why? Because 90% of the energy used to light an incandescent bulb is given off as heat. Incandescent light bulbs are
very inefficient (if you’re interested in the light from the bulb and not the heat!). The Joule heating of energy-efficient
light bulbs is considerably less, and therefore requires a smaller amount of energy to produce the same amount of
light.Illustrative Example 18.3.1a. A 10Ωhas^14 Wrating. Meaning, any power greater than this will burn the resistor out.
Will the resistor burn out if it is connected to a 6. 0 Vbattery?
Solution:
The current through the resistor must be found in order to answer the question. Using Ohm’s law we have:V=IR→ 6. 0 V=I( 10 Ω)→I=^610.^0 .VΩ= 0. 60 A
P=IV= ( 0. 60 A)( 6. 0 V) = 3. 6 W
The resistor will definitely burn out.
b. What is the maximum current that the resistor can handle without burning out?
Answer:
P=I^2 R→I=√
P
R=√
0. 25 W
10 Ω =^0.^158 =^0.^16 A
c. What is the maximum voltage drop across the resistor?
Answer:V=IR= ( 0. 158 A)( 10 Ω) = 1. 58 → 1. 6 V
Illustrative Example 18.3.2a. Determine the equivalent resistance of the circuit below.