determine the value of R?

the resistor in the figue recieves 20W power. 

Attachment image

2 Answers

Relevance
  • 4 weeks ago
    Favorite Answer

    Total resistance of the branch on the right = 40 + R [1]

    Resistance of 30 ohms in parallel with that = 30(40+R)/(30 + 40 + R) = 30(40+R)/(70+R) [2]

    The 5 ohm and [2] 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)) [3]

    the 40 ohm and R form a voltage divider, so the voltage across R is R/(40+R) of [3], or

    V = 75 * (30(40+R)/(70+R)) / (5 + 30(40+R)/(70+R)) * R/(40+R) [4]

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

    20 = V^2 / R [5]

    R = V^2/20 [6]

    Substitue [6] for R into [4], then solve for V.  Once you have V, sustitute back into [6] to find R.

  • 4 weeks ago

    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

    using a quad. solver

    R = 126, 13.9 ohms

    but check my math.

Still have questions? Get your answers by asking now.