A pure resistance and a pure inductance are connected in series across a 100V (rms) AC line. An AC voltmeter gives the same reading when connected across either the R or the L. What does it read? (note: meters read rms values)

Question

anonymous · Answer

@wio

anonymous · Answer

Sorry I'm kinda busy right now

anonymous · Answer

it's okay

kropot72 · Answer

The equal voltages are 90 degrees out of phase.
|dw:1364197089669:dw|
$$\cos 45\deg=\frac{V _{R}}{100}$$
Can you find the voltmeter reading now?

kropot72 · Answer

@Lynncake Are you there?

anonymous · Answer

@kropot72 i got the value to be 70.71 Is this right? and why is the angle 45 degrees?

kropot72 · Answer

Yes the voltages across the R and the L are equal with value
$$\frac{100}{\sqrt{2}}$$
In this case the applied voltage is the vector sum of the voltages across the R and the L and has the phase angle 45 degrees with respect to the circuit current.

anonymous · Answer

So, if the magnitudes of R and L are altered so that the voltmeter across L reads 50V. The voltmeter that is read across R is 86.6 |dw:1364199781741:dw|$$\sqrt{100^2 - (50)^}$$