Resistance in series, Rs = 5 ohm
Total power of the circuit, P = 1200 watts
Total resistance in parallel combination, Rp = 10 ohm



To find the value of R, we first need to calculate the equivalent resistance of the parallel combination.

We know that the total resistance in a parallel combination is given by the formula:

1/Rp = 1/R1 + 1/R2

Substituting the given values, we have:

1/Rp = 1/R + 1/10

To simplify the equation, we can find the common denominator:

1/Rp = (10 + R)/(10R)

Taking the reciprocal of both sides of the equation:

Rp = (10R)/(10 + R)


The total resistance of the circuit is the sum of the resistance in series (Rs) and the resistance of the parallel combination (Rp).

Rtotal = Rs + Rp

Substituting the given values, we have:

Rtotal = 5 + (10R)/(10 + R)


To find the value of R, we need to solve the equation Rtotal = 5 + (10R)/(10 + R) for R.

Multiplying both sides of the equation by (10 + R), we get:

Rtotal(10 + R) = 5(10 + R) + 10R

Expanding the equation:

10R + R^2 + 10R = 50 + 5R + 10R

Simplifying the equation:

R^2 + 10R + 10R - 5R - 10R - 50 = 0

R^2 + 5R - 50 = 0

Using the quadratic formula, we can solve for R:

R = (-b ± √(b^2 - 4ac))/(2a)

In this case, a = 1, b = 5, and c = -50.

R = (-5 ± √(5^2 - 4(1)(-50)))/(2(1))

R = (-5 ± √(25 + 200))/(2)

R = (-5 ± √(225))/(2)

R = (-5 ± 15)/(2)

R = (-5 + 15)/(2) or R = (-5 - 15)/(2)

R = 10/2 or R = -20/2

R = 5 or R = -10

Since resistance cannot be negative, the value of R is 5 ohm.

Therefore, the value of R is 5 ohm.