(a) 273.9 V
The power rating of the resistor is given by
where
P is the power rating
V is the potential difference across the resistor
R is the resistance
If the maximum power rating is , and the resistance of the resistor is
, then we can find the maximum potential difference across the resistor by re-arranging the previous equation for V:
(b) 1.6 W
In this case, we have:
is the resistance of the resistor
is the potential difference across the resistor
So we can find the power rating by using the same formula of part (a):
(c) Maximum voltage: 14.1 V; Rate of heat: 2.00 W and 3.00 W
Here we have two resistors of
and each resistor has a power rating of
P = 2.00 W
So the greatest potential difference allowed in the first resistor is
While the greatest potential difference allowed in the second resistor is
So the greatest potential difference allowed not to overheat either of the resistor is 14.1 V.
In this condition, the power dissipated on the first resistor is 2.00 W, while the power dissipated on the second resistor is
And this corresponds to the rate of heat generated in the first resistor (2.00 W) and in the second resistor (1.33 W).