A 0.1\mu F capacitor charged to 100 V is discharged through a 1 k\Omega resistor. The time in ms (round off to two decimal places) required for the voltage across the capacitor to drop to 1V is ______
\begin{aligned} v_c(t)&=V_0e^{-t/\tau } \\ V_0&=100V \\ \tau &=RC=(10^3)(10^{-7}) \\ &=10^{-4}sec \\ \therefore \;v_c(t)&=100e^{-10^4 t }V \end{aligned} Let the time required by the voltage across the capacitor to drop to 1 V is t_1, \begin{aligned} \therefore \; v_c(t_1)&=100e^{-10^4t_1} \\ \text{But, } v_c(t_1)&=0 \\ \text{So, }0&=100e^{-10^4t_1} \\ t_1&=0.46msec \end{aligned}
Question 2
The voltage across the circuit in the figure, and the current through it, are given by the
following expressions: v(t) = 5 - 10 cos(\omega t + 60^{\circ}) V i(t) = 5 + X cos(\omega t) A
where \omega =100 \pi radian/s. If the average power delivered to the circuit is zero, then the
value of X (in Ampere) is _____ (up to 2 decimal places).
In the figure, the voltages are v_{1}(t)=100cos(\omega t), v_{2} (t) = 100cos(\omega t + \pi /18) and v_{3}(t) = 100cos(\omega t + \pi /36). The circuit is in sinusoidal steady state, and R \lt \lt \omega L. P_{1},P_{2} and P_{3} are the average power outputs. Which one of the following statements is true?
V_2:\frac{\pi}{18}=\frac{180^{\circ}}{18}=10^{\circ} V_3:\frac{\pi}{36}=\frac{180^{\circ}}{36}=5^{\circ} V_2 leads V_1 and V_3, So, V_2is a source, V_1 and V_3 are absorbing. Hence, P_2 \gt 0 and P_1,P_3 \lt 0
Question 4
The voltage (V) and current (A) across a load are as follows. v(t) = 100 sin(\omega t), i(t) = 10 sin(\omega t - 60^{\circ}) + 2 sin(3\omega t) + 5 sin(5\omega t).
The average power consumed by the load, in W, is___________.
The average power consumed by the load = P=V_1I_1 \cos \phi \;\;=\frac{100}{\sqrt{2}}\frac{10}{\sqrt{2}} \cos 60^{\circ}=250W
Question 5
A resistance and a coil are connected in series and supplied from a single phase, 100 V, 50 Hz ac source as shown in the figure below. The rms values of plausible voltages across the resistance (V_{R})
and coil (V_{C}) respectively, in volts, are
As per GATE Official answer key MTA (Marks to All)
Question 6
In the circuit shown below, the supply voltage is 10sin(1000t) volts. The peak value of the steady state current through the 1\Omega resistor, in amperes, is ______.
If we observe the parallel LC combination, we get that at \omega=1000 rad/sec the parallel LC is at resonance, thus it is open circuited. The circuit given in question can be redrawn as So, I=\frac{10 \sin 1000t}{10}=\sin 100t So, peak value is 1 Amp.
Question 7
A symmetrical square wave of 50% duty cycle has amplitude of \pm15 V and time period of 0.4\pi ms. This square wave is applied across a series RLC circuit with R=5 \Omega, L=10 mH, and C=4 \muF. The amplitude of the 5000 rad/s component of the capacitor voltage (in Volt) is ______.
Given, total power dissipated in the circuit = 1kW =1000 Watt \therefore \;\; 2^2 \times 1 +10^2 \times R=1000 R=\frac{998}{100}=9.98\Omega Also, voltage drop across R, V_R=IR =10 \times 9.98=99.8 volt Voltage drop across load, V=200 volt =\sqrt{V_R^2+V_{X_L}^2} \therefore voltage drop across inductor, V_{X_L}=\sqrt{V^2-V_R^2} \;\;=\sqrt{(200)^2-(99.8)^2} \;\;=173.32 volt Now, V_{X_L}=IX_L X_L=\frac{V_{X_L}}{I} X_L=\frac{173.32}{10}=17.332\Omega
Question 9
In the circuit shown, the three voltmeter readings are V_1=220 V , V_2=122 V , V_3=136 V. If R_L=5\Omega, the approximate power consumption in the load is