The diode in the circuit shown below is ideal. The input voltage (in Volts) is given by \[ V_I = 10 \sin(100\pi t), \quad {where time} \, t \, {is in seconds.} \] The time duration (in ms, rounded off to two decimal places) for which the diode is forward biased during one period of the input is (answer in ms).
Two fair dice (with faces labeled 1, 2, 3, 4, 5, and 6) are rolled. Let the random variable \( X \) denote the sum of the outcomes obtained. The expectation of \( X \) is _________ (rounded off to two decimal places).
All the diodes in the circuit given below are ideal. Which of the following plots is/are correct when \( V_I \) (in Volts) is swept from \( -M \) to \( M \)?
For the circuit shown in the figure, the active power supplied by the source is ________ W (rounded off to one decimal place).
A signal $V_M = 5\sin(\pi t/3) V$ is applied to the circuit consisting of a switch S and capacitor $C = 0.1 \mu F$, as shown in the figure. The output $V_x$ of the circuit is fed to an ADC having an input impedance consisting of a $10 M\Omega$ resistance in parallel with a $0.1 \mu F$ capacitor. If S is opened at $t = 0.5 s$, the value of $V_x$ at $t = 1.5 s$ will be ________ V (rounded off to two decimal places).
Note: Assume all components are ideal.
In the circuit shown, the switch is opened at $t = 0$ s. The current $i(t)$ at $t = 2$ ms is ________ mA (rounded off to two decimal places).
In the circuit shown, the galvanometer (G) has an internal resistance of $100 \Omega$. The galvanometer current $I_G$ is ________ $\mu A$ (rounded off to the nearest integer).
The circuit given in the figure is driven by a voltage source $V_s = 25\sqrt{2}\angle 30^\circ V$. The system is operating at a frequency of 50 Hz. The transformers are assumed to be ideal. The average power dissipated, in W, in the $50 k\Omega$ resistance is ________ (rounded off to two decimal places).