Question

the power across a 75 ohm resistor is 90w find the value of the resistance to be connected in series with 75 ohm across a supply voltage of 120 v

Answer 1

the power across a 75 ohm resistor is $90\mathrm{w}$ and the value of the resistance to be connected in series with 75 ohm across a supply voltage of $120\mathrm{v}$

Solution

The power across two resistors connected in series is

$$P = \frac {U ^ {2}}{R _ {1} + R _ {2}} = 90\mathrm{w},$$

where U - a supply voltage of $120\mathrm{v}$, $R_{1}$ - a 75 ohm resistor, $R_{2}$ - the value of the resistance of second resistor.

We have

$$R _ {2} = \frac {U ^ {2}}{P} - R _ {1} = \frac {120^{2}}{90} - 75 = 85\mathrm{ohm}.$$

Answer: 85 ohm.