A 20 ohm resistor with a current of 0.25 A passing through it will dissipate how many watts? 20 watts 1.25 watts 10 watts 0.025 watts
The correct answer and explanation is:
The correct answer is 1.25 watts.
To determine the power dissipated by a resistor, we use the formula for electrical power: P=I2×RP = I^2 \times R
Where:
- PP is the power dissipated (in watts),
- II is the current (in amperes),
- RR is the resistance (in ohms).
In this case, the current I=0.25 AI = 0.25 \, \text{A} and the resistance R=20 ΩR = 20 \, \Omega.
Substitute the given values into the formula: P=(0.25)2×20P = (0.25)^2 \times 20 P=0.0625×20=1.25 wattsP = 0.0625 \times 20 = 1.25 \, \text{watts}
So, the resistor dissipates 1.25 watts of power.
Explanation
Power dissipation in a resistor is the amount of energy per second that is converted into heat due to the resistance to the flow of electric current. The power can be calculated using Ohm’s law (which relates current, voltage, and resistance) and is given by P=I2×RP = I^2 \times R.
This formula implies that the power dissipated in the resistor increases with the square of the current. If the current were to increase, the power dissipation would increase significantly. Similarly, the power dissipation also increases as the resistance increases, for a given current.
For comparison, using the other formula for power, P=V2/RP = V^2 / R, where VV is the voltage across the resistor, you could calculate power if voltage was given. In this case, though, the formula P=I2×RP = I^2 \times R directly leads to the correct answer, 1.25 watts.