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Chapter 14: Problem 2064

\(220 \mathrm{~V}, 50 \mathrm{~Hz}\), ac is applied to a resistor. The instantaneous value of voltage is (a) \(220 \sqrt{2} \sin 100 \pi \mathrm{t}\) (b) \(220 \sin 100 \pi \mathrm{t}\) (c) \(220 \sqrt{2} \sin 50 \pi \mathrm{t}\) (d) \(220 \sin 50 \pi \mathrm{t}\)

Short Answer

Expert verified
The correct instantaneous value of voltage is (a) \(220 \sqrt{2} \sin 100 \pi \mathrm{t}\).

Step by step solution

01

Calculate Maximum Voltage (V_m)

To find the maximum voltage, we need to use the relation between RMS voltage and maximum voltage. The relation is as follows: \[V_{rms} = \frac{V_m}{\sqrt{2}}\] Now, we can calculate the maximum voltage \((V_m)\) : \[V_m = V_{rms} \times \sqrt{2}\] \[V_m = 220\sqrt{2} \mathrm{~V}\]
02

Calculate the Angular Frequency (ω)

To find the angular frequency, we need to use the relation between frequency and angular frequency. The relation is as follows: \[\omega = 2\pi f\] Where \(f\) is the frequency. Now, we can calculate the angular frequency \((\omega)\): \[\omega = 2\pi (50) = 100\pi\]
03

Form the Instantaneous Voltage Equation

Now that we have calculated the maximum voltage \((V_m)\) and angular frequency \((\omega)\), we can write the equation of the instantaneous voltage: \[V(t) = V_m \sin(\omega t)\] \[V(t) = 220\sqrt{2} \sin(100\pi t)\] This matches with option (a). Therefore, the correct answer is: (a) \(220 \sqrt{2} \sin 100 \pi \mathrm{t}\)

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Most popular questions from this chapter

In an ac circuit the emf (e) and the current (i) at any instant core given respectively by \(\mathrm{e}=\mathrm{E}_{\mathrm{O}}\) sin $\operatorname{ct}, \mathrm{I}=\mathrm{I}_{\mathrm{O}} \sin (\cot -\Phi)$. The average power in the circuit over one cycle of ac is. (a) \(\left[\left\\{E_{O} I_{O}\right\\} / 2\right] \cos \Phi\) (b) \(\mathrm{E}_{\mathrm{O}} \mathrm{I}_{\mathrm{O}}\) (c) \(\left[\left\\{E_{Q} I_{Q}\right\\} / 2\right]\) (d) \(\left[\left\\{E_{O} I_{O}\right\\} / 2\right] \sin \Phi\)

The instantaneous voltage through a device of impedance \(20 \Omega\) is \(\varepsilon=80 \sin 100 \pi t\). The effective value of the current is, (a) \(3 \mathrm{~A}\) (b) \(2.828 \mathrm{~A}\) (c) \(1.732 \mathrm{~A}\) (d) \(4 \mathrm{~A}\)

A transformer of efficiency \(90 \%\) draws an input power of \(4 \mathrm{~kW}\). An electrical appliance connected across the secondary draws a current of $6 \mathrm{~A}$. The impedance of device is ....... (a) \(60 \Omega\) (b) \(50 \Omega\) (c) \(80 \Omega\) (d) \(100 \Omega\)

The magnetic flux linked with a coil, in webers, is given by the equation \(\Phi=4 t^{2}-t+7\). Then the magnitude of induced emf at 2 sec will be ... (a) \(15 \mathrm{v}\) (b) \(19 \mathrm{v}\) (c) \(17 \mathrm{v}\) (d) \(21 \mathrm{v}\)

An LC circuit contains a \(20 \mathrm{mH}\) inductor and a \(50 \mu \mathrm{F}\) capacitor with an initial charge of \(10 \mathrm{mc}\). The resistance of the circuit is negligible. At the instant the circuit is closed be \(t=0 .\) At what time is the energy stored completely magnetic. (a) \(\mathrm{t}=0 \mathrm{~ms}\) (b) \(\mathrm{t}=1.54 \mathrm{~ms}\) (c) \(\mathrm{t}=3.14 \mathrm{~ms}\) (d) \(\mathrm{t}=6.28 \mathrm{~ms}\)
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