Resistor, capacitor and coil with Alternating current

[Karol]

Homework Statement

A problem from a translated Sears-Zemansky, 1965, 14-10:
A conduction coil with inductance of 15 miliHenrys and resistance of 10 Ohms, is connected in line with a capacitor of 200 microFarads and a resistor of 12 Ohms.
The circuit is supplied with an alternating current of 100 Volts and frequency 50 cycles/sec.
What is the voltage between the terminals of the conduction coil?

Homework Equations

<br /> \begin{equation*}<br /> \begin{split}<br /> \omega &amp;=2\pi L \\<br /> X_{L} &amp;=\omega C \\ <br /> X_{C} &amp;=\frac{1}{{\omega} C} \\<br /> X &amp;=X_{L}-X_{C} \\<br /> Z &amp;=\sqrt{R^{2}+X^{2}} \\<br /> V_{active} &amp;=I_{active}\times Z<br /> \end{split}<br /> \end{equation*}<br />

The Attempt at a Solution

<br /> \begin{equation*}<br /> \begin{split}<br /> X_{L} &amp;=2\pi 50 \cdot 0.015=4.7 \\<br /> X_{C} &amp;=\frac{1}{2\pi 50 \cdot 2\times 10^{-4}}=15.9 \\<br /> X &amp;=4.7-15.9=-11.2 \\<br /> Z &amp;=\sqrt{22^{2}+(-11.2)^{2}}=24.7<br /> \end{split}<br /> \end{equation*}<br />

The total active current in the circuit is found from the total active voltage equation:

100=I \cdot 24.7 \Rightarrow I=4.05

The "Resistance" (I don't know how it is called in English, please tell me) Z on the conduction coil itself (with its resistance) is:

Z=\sqrt{R^{2}+X^{2}_L}=\sqrt{10^{2}+4.7^{2}}=11

And the voltage on the coil is, using the total current in the circuit, calculated above:

V=I \times Z=4.05 \cdot 11=44.8

The answer should be: 49.4 [Volts]
Where is the mistake?
Thanks-Karol

 

[ehild]

Your calculation is correct, but take care of rounding: use at least as many significant digits during the calculations as in the result.

ehild

 

[Karol]

Thanks, I'l do that.