The value of impedance Z of the circuit, when the rate at which electrical energy is dissipated in the resistor is 316 w, is 508 ohms.
The impedance Z of the circuit is the ratio of voltage amplitude to the maximum current.
[tex]Z=\dfrac{V}{I}[/tex]
Here, V is voltage amplitude and I maximum current.
A resistor with R = 300 Ω and an inductor are connected in series across an ac source that has voltage amplitude 490V. The rate at which electrical energy is dissipated in the resistor is 316 W.
The rate at which electrical energy is dissipated in the resistor is the product of the resistance and the square of current. Thus,
[tex]316=340\times I^2\\I=\sqrt{\dfrac{316}{340}}\\I=0.964\rm\; A[/tex]
The impedance Z of the circuit is,
[tex]Z=\dfrac{V}{I}\\Z=\dfrac{490}{0.964}\\Z=508\rm\; ohm[/tex]
Thus, the value of impedance Z of the circuit, when the rate at which electrical energy is dissipated in the resistor is 316 w, is 508 ohms.
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