# determine the value of R?

the resistor in the figue recieves 20W power. Relevance

Total resistance of the branch on the right = 40 + R 

Resistance of 30 ohms in parallel with that = 30(40+R)/(30 + 40 + R) = 30(40+R)/(70+R) 

The 5 ohm and  form a voltage divider, so voltage on the non-battery side of the 5 ohm is

75 * (30(40+R)/(70+R)) / (5 + 30(40+R)/(70+R)) 

the 40 ohm and R form a voltage divider, so the voltage across R is R/(40+R) of , or

V = 75 * (30(40+R)/(70+R)) / (5 + 30(40+R)/(70+R)) * R/(40+R) 

But the power in R is 20 W.  Remembering that P = V^2/R,

20 = V^2 / R 

R = V^2/20 

Substitue  for R into , then solve for V.  Once you have V, sustitute back into  to find R.

• thevenin equivalent, terminals at R

Rth = 5 parallel 30 in series with 40

Rth = 5•30/35 + 40 = 30/7 + 40 = 44.3 Ω

Vth = 75(30/35) = 64.3 volts

Voltage across R = 64.3R/(44.3+R)

current thru R = V/R = 64.3/(44.3+R)

power is the product

64.3R/(44.3+R) x 64.3/(44.3+R) = 20

(64.3/(44.3+R))²(R+1) = 20

(4133/(1961+66.6R+R²))(R+1) = 20

20(1961+66.6R+R²) = 4133(R+1)

39220 + 1332R + 20R² = 4133R + 4133

20R² – 2801R + 35087 = 0