The current flowing through an AC circuit is given by
\(I=5 \sin (120 \pi t)~\text{A}\) 
How long will the current take to reach the peak value starting from zero? 
1. \(\frac{1}{60}~\text{s} \)
2. \(60~\text{s} \)
3. \(\frac{1}{120}~\text{s} \)
4. \(\frac{1}{240}~\text{s} \)

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What material is used to make the core of a transformer?
1. Copper
2. Aluminium
3. Soft iron
4. Steel
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The correct representation of the variation of capacitative reactance \(X_C\) with frequency \(f\) is:
1.   2.  
3.   4.  
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The core of the transformer is laminated so that:
1. the copper loss is minimized.
2. the eddy current loss is minimized.
3. the rusting of the core is stopped.
4. the change in flux is increased.
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A transmission line feeds input power at \(2200~\text{V}\) to a step-down transformer having a primary winding of \(1000\) turns. To get the output power at \(220~\text{V},\) the number of turns in the secondary winding will be:
1. \(50\)
2. \(100\)
3. \(1000\)
4. \(10000\)
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A resistance of \(5~\Omega\) is connected in series with a capacitance of \(1~\text{mF}\). The combination is connected to an AC source of angular frequency \(200~\text{rad/s}\). Then:
1. voltage leads the current by \(60^\circ\)
2. current leads the voltage by \(60^\circ\)
3. current leads the voltage by \(45^\circ\)
4. voltage leads the current by \(45^\circ\)
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In a series \(LCR\) circuit, the inductance, capacitance and resistance are \(L = 100~\text{mH}\), \(C = 100~\mu\text{F}\) and \(R =10~\Omega\) respectively. They are connected to an AC source of voltage \(220~\text{V}\) and frequency of \(50~\text{Hz}\). The approximate value of current in the circuit will be:
          
1. \(15~\text{A}\)
2. \(32~\text{A}\)
3. \(22~\text{A}\)
4. \(14~\text{A}\)
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A sinusoidal voltage \(V(t) = 210\sin(3000 t)~\text{V}\) is applied to a series \(LCR\) circuit in which \(L = 10~\text{mH}\), \(C= 25~\mu\text{F}\) and \(R = 100~\Omega\). The phase difference \((\phi)\) between the applied voltage and resultant current will be:
1. \(\text{tan}^{-1}(0.17)\)
2. \(\text{tan}^{-1}(9.46)\)
3. \(\text{tan}^{-1}(0.30)\)
4. \(\text{tan}^{-1}(13.33)\)
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A step-down transformer operates on \(2\) kV line. The ratio of the primary winding to the secondary winding is \(20:1\). Assuming \(100\%\) efficiency, the secondary voltage \(V_2\) is:
1. \(100~\text V\)
2. \(110~\text V\)
3. \(200~\text V\)
4. \(250~\text V\)
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A \(100~\text{V},\) \(50~\text{Hz} \text-\) AC voltage source is connected across a \(2~\mu\text{F}\) capacitor. The current in the circuit is:
1. \(42\) mA
2. \(62.8\) mA
3. \(200\) mA
4. \(300\) mA
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