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#4 | RMS Value of Alternating Current & Voltage
(Physics) > Alternating Current

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An alternating current is given as \(i = i_1 \cos\omega t+i_2\sin\omega t\). The RMS current is given by;
1. \(\dfrac{i_1+i_2}{\sqrt{2}}\)
2. \(\dfrac{(i_1+i_2)^2}{\sqrt{2}}\)
3. \(\sqrt{\dfrac{i_1^2+i^2_2}{2}}\)
4. \(\dfrac{\sqrt{i_1^2+i^2_2}}{2}\)

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A generator produces a voltage that is given by V = 240 sin 120 t, where t is in seconds. The frequency and r.m.s. voltage are 

(1) 60 Hz and 240 V

(2) 19 Hz and 120 V

(3) 19 Hz and 170 V

(4) 754 Hz and 70 V

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A resistance of \(20~ \Omega\) is connected to a source of an alternating potential, \(V=220\sin(100 \pi t).\) The time taken by the current to change from its peak value to its rms value will be: 
1. \( 0.2~\text{sec}\) 2. \( 0.25~\text{sec}\)
3. \(25 \times10^{-3}~\text{sec}\) 4. \(2.5 \times10^{-3}~\text{sec}\)
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The variation of the instantaneous current \((I)\) and the instantaneous emf \((E)\) in a circuit are shown in the figure. Which of the following statements is correct?

         

1. The voltage lags behind the current by \(\frac{\pi}{2}\).
2. The voltage leads the current by \(\frac{\pi}{2}\).
3. The voltage and the current are in phase.
4. The voltage leads the current by \(\pi\).
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The output current versus time curve of a rectifier is shown in the figure. The average value of the output current in this case will be:
       

1. \(0\) 2. \(I_0 \over 2\)
3. \(2I_0 \over \pi\) 4. \(I_0\)
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