CALCULATION OF THE POWER ABSORBED BY A RESISTOR
A new quiz by Online Technologies for Beginners.
Two circuits are assigned consisting of a DC voltage generator to which a resistor is connected.
You are asked to indicate which resistor absorbs the most power.
SOLUTION
The exercise is designed in such a way as to induce the novice to think that the two resistors are absorbing equal power.
This arises from the fact that the current flowing in the first circuit has the same intensity as the current flowing in the second circuit.
Applying Ohm’s law to the first circuit, we have that the circulating current is equal to I1 = 12V/3Ohm = 4 A
Similarly, applying Ohm’s law to the second circuit, we have that the circulating current is equal to I2 = 24V/6Ohm = 4 A
The fact that the two circuits are crossed by a current of equal intensity does not imply that the power absorbed by the resistors is the same.
It should in fact be remembered that the power absorbed by the load is obtained by the product of the voltage applied to the load multiplied by the current flowing through the load.
In the first circuit we therefore have that the power absorbed by R1 is equal to:
P1 = V1 · I1 =
12 V · 4 A = 48 W
In the second circuit we therefore have that the power absorbed by R2 is equal to:
P2 = V2 · I2 =
24 V · 4 A = 96 W
We therefore observe that the second resistor absorbs a greater power than the first resistor and therefore the correct answer is B.
In fact, R2 is crossed by a current equal to that flowing through R1, but a lower voltage is applied to the latter and therefore will absorb less power.
Another way to calculate the power absorbed by the resistor is to calculate the ratio between the applied voltage raised to the square and the resistance of the resistor expressed in ohms.
If we carry out the calculations, we get that:
P1=48W
and
P2=96W
The two power values obtained are identical to those obtained with the first method and therefore we can confirm that the correct answer is “B”.
In particular, the resistor R2 absorbs a double power (96 W) compared to that absorbed by the resistor R1 (48 W).
