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 \( M \)?
In the given circuit with ideal diodes, the current-voltage relationship will change depending on the input voltage (\(V_I\)). The behavior of the circuit can be broken down into the following steps:
Step 1: Diode behavior when \(V_I\) is negative
When \(V_I\) is negative, the diodes will be reverse biased and no current will flow through the circuit. Therefore, the output voltage \(V_o\) will be 0 for negative \(V_I\), and the plot will be flat from \(-M\) to 0.
Step 2: Diode behavior when \(V_I\) is positive
When \(V_I\) is positive, the diodes will conduct and the output voltage will increase linearly with \(V_I\). This results in a linear relationship between \(V_o\) and \(V_I\) for positive \(V_I\). The correct plot is (A) for the output voltage and (D) for the current \(I_I\) in the circuit, where the current increases as \(V_I\) increases.
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).
Consider a part of an electrical network as shown below. Some node voltages, and the current flowing through the \( 3\,\Omega \) resistor are as indicated.
The voltage (in Volts) at node \( X \) is _________.
The 12 musical notes are given as \( C, C^\#, D, D^\#, E, F, F^\#, G, G^\#, A, A^\#, B \). Frequency of each note is \( \sqrt[12]{2} \) times the frequency of the previous note. If the frequency of the note C is 130.8 Hz, then the ratio of frequencies of notes F# and C is:
A 4-bit weighted-resistor DAC with inputs \( b_3, b_2, b_1, \) and \( b_0 \) (MSB to LSB) is designed using an ideal opamp, as shown below. The switches are closed when the corresponding input bits are logic ‘1’ and open otherwise. When the input \( b_3b_2b_1b_0 \) changes from 1110 to 1101, the magnitude of the change in the output voltage \( V_o \) (in mV, rounded off to the nearest integer) is _________.