Determine the value of Resistance:
Determine the value of R, so that the condition for resonance is fulfilled
Figure
Solution
Admittance of first branch
Y_{1} = 1/ R - 5 j = R - 5 j/ R^{2 }+ 25 mho
Admittance of second branch
Y_{2} = 1 / (4 - 3 j) = ((4 + 3 j)/25) mho
Total admittance of the circuit:
Y = Y_{1 }+ Y_{2} = (R - 5 j / R_{2} + 25) + ((4 + 3 j)/25)
According to condition of resonance the imaginary part of the admittance must be zero i.e.
- 5/ (R^{2} + 25) + (3/25) = 0
5/ (R^{2} + 25) = 3/25
⇒ R = 4.082 Ω