Determine the value of Resistance:

Determine the value of R, so that the condition for resonance is fulfilled

Figure

Solution

Admittance of first branch

Y₁ = 1/ R - 5 j = R - 5 j/ R² + 25 mho

Admittance of second branch

Y₂ = 1 / (4 - 3 j) = ((4 + 3 j)/25) mho

Total admittance of the circuit:

Y = Y₁ + Y₂ =   (R - 5 j / R₂ + 25) + ((4 + 3 j)/25)

According to condition of resonance the imaginary part of the admittance must be zero i.e.

- 5/ (R² + 25) + (3/25) = 0

     5/ (R² + 25) = 3/25

⇒      R = 4.082 Ω