EasyPhysicsHigh School (11–12)Electricity & Magnetism › Alternating CurrentNumericalBoard ExamA-LevelIB
In a series LCR circuit, a voltmeter across the resistor reads 24 V…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
In a series LCR circuit, a voltmeter across the resistor reads V. Across the coil it reads V, and across the capacitor V. All are rms readings. What does a voltmeter across the source read? By what angle does the current lag behind the source voltage?
Need a reminder? The key ideaShow
In a series circuit the same current flows in every part. The reactances are and , with . The impedance is , and holds for peak or for rms values. The phase is . A positive means the current lags.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Given. V, V and V.
Plan. The voltages of the coil and the capacitor are apart, so we subtract them. We then add the result to as the other side of a right triangle.
Step 1. The net reactive voltage. V.
Step 2. The source voltage. V.
Step 3. The phase. , so . It is positive, so the current lags.
Answer: V, and the current lags by .
Watch out. The three readings add to V, but the source voltmeter reads V. Voltmeter readings do not add like plain numbers.
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