Calculation of Resonant Frequency
The resonant frequency of the circuit can be calculated using the formula:
f = 1/2π√(LC)
Substituting the given values, we get:
f = 1/2π√(10mH x 0.01μF)
f = 1591.55 Hz

Determination of Impedance
The impedance of the circuit at resonance can be calculated using the formula:
Z = R
Substituting the given value of R, we get:
Z = 50Ω

Calculation of Current
The current flowing through the circuit can be calculated using the formula:
I = V/Z
Substituting the given values of V and Z, we get:
I = 10sinwt/50
I = 0.2sinwt

Calculation of Power Dissipation
The power dissipated in the circuit can be calculated using the formula:
P = I^2 x R
Substituting the values of I and R, we get:
P = (0.2sinwt)^2 x 50
P = 2.5sin^2(wt) W

Explanation
In a series RLC circuit, the inductor (L), capacitor (C), and resistor (R) are connected in series with each other. The circuit is supplied with an AC voltage source, and the current flowing through the circuit depends on the values of L, C, and R. At a certain frequency known as the resonant frequency, the impedance of the circuit becomes minimum, and the current flowing through the circuit becomes maximum. At resonance, the voltage across the resistor (R) is maximum, and this is where the power dissipated in the circuit is maximum. In this question, we have calculated the resonant frequency, impedance, current, and power dissipation in the circuit. The power dissipated in the circuit is proportional to the square of the current flowing through the circuit.