Question

Find the V_rms across each of the three elements when a 10 ohms resistor, 10mH inductor and 10nF capacitor are connected in series with a 10MHz voltage source. The rms current through the circuit is 0.50A.

Answer 1

The total impedance in the series RLC circuit is

$\displaystyle Z = \sqrt{R^2 + (\omega L -\frac{1}{\omega C})^2} = \sqrt{100 + (10^7 \cdot10 ^{-2} -\frac{1}{10^{7} \cdot 10^{-8}})^2} = \sqrt{100+ (10^5-10)^2} = 10^5\; \Omega$

Then

$\displaystyle V_{rms} = \frac{I_{rms}}{Z} = \frac{0.5 A}{10^5 \Omega} = 5 \cdot 10^{-6} \; V = 5 \; \mu V$

Answer: $5 \; \mu V$