91影视

1. Current in the RLC circuit,$I_s=4.00\text{A}$
2. Inductance of the circuit,$L=200\text{渭贬}$
3. Emf amplitude,$V=8.0\text{V}$

When the driving frequency of the circuit becomes equal to the natural frequency of the circuit, a phenomenon known as resonance occurs in the circuit. In this state, the inductive reactance becomes equal to the capacitive reactance.

We use the angular frequency formula to find the capacitance of the capacitor. Using Ohm鈥檚 law, we can find the resistance.

The angular frequency of an LC oscillation,

${蝇}_d=\frac{1}{\sqrt{LC}}$ ...(i)

The voltage equation using Ohm鈥檚 law,

$V=IR$ ...(ii)

Here, $C$is the capacitance of the capacitor, $I$is the inductance of the inductor, $R$is the resistance of the resistor and $I$is the current in the circuit.

Where the angular frequency of the circuit is equal to${蝇}_d=1/\sqrt{LC,}$the current is maximum. Thus, using the given data in equation (i), we can get the value of the capacitance of the circuit as follows:

$$\begin{gathered} \text{C=}\frac{1}{{蝇}_d^{2}L} \\ =\frac{1}{{\left(25000\text{rad/s}\right)}^2脳\left(200脳{10}^{-6}\text{H}\right)} \\ =8.00\text{渭贵} \end{gathered}$$

Hence, the value of the capacitance is $8.00\text{渭贵}$.

When the current is maximum, the impedance of the current is equal to the resistance of the circuit. Thus, using the above impedance value and equation (ii), we can get the value of the resistance as follows:

$$\begin{gathered} Z=R \\ =\frac{V}{I} \\ =\frac{8.0\text{V}}{4.00\text{A}} \\ =2.00\text{惟} \end{gathered}$$

Hence, the value of the resistance is localid="1662792302789" $2.00\text{惟}$.