Using mesh analysis calculate the three mesh currents i1 i2

Question

Answer the following questions -

Q1. Circuit Analysis

a) Using Mesh analysis:

i. Calculate the three mesh currents, I₁, I₂ and I₃, of the network shown in Figure 1,

ii. Calculate the current I_R2 through R₂,

iii. Calculate the voltage V_R5 across R₅.

State clearly the directions of the currents and the polarity of the voltage. Show the derivation of the mesh equations. Solve them using a software tool of your choice (e.g. wolframalpha.com) including a screen shot of the results.

The values of V₁ and V₂ are the last two non-zero digits of your student ID (eg. If your student ID is 7256105, then V₁ = 1 and V2=5).

Q2. Operational Amplifiers

a) The circuit shown in Figure 2 performs the following operation v₀ = A₁v₁ + A₂v₂ where A₁ and A₂ are the last two non-zero digits of your student ID:

i) A₂ is the smallest digit,

ii) A₁ is the largest digit if both digits are different, or, A₁ = A₂ + 1 if both digits are identical.

(You should always have A₁ > A₂).

Given that R₁ = 1.8 kΩ, R_c = 2 kΩ, R_f2 = 12kΩ, and that R₂ = R₃, calculate the values for R₂ and R_f1 to achieve the desired operation.

Q3. RLC circuits, Resonance and Filters

A RLC series circuit contains a resistance R, an inductor L and a capacitor C. It is driven by a 230 V rms variable frequency AC voltage source. The value of R, C and L are given in Table 1 against the last digit of your student ID.

a) Calculate the resonance frequency (f_r) of the circuit and then calculate the following under resonant condition:

i) The individual inductive (X_L) and capacitive reactance (X_C) and the total impedance (Z) of the circuit.

ii) The circuit current and the voltage across each component.

iii) The power dissipation at the cut-off frequency.

Last Digit ofStudent ID	R(Ω)	L (mH)	C(µf)
0	5	12	4
1	10	15	2
2	5	22	6
3	10	18	8
4	5	10	10
5	10	20	7
6	5	12	24
7	10	15	10
8	5	20	8
9	10	12	14

Table 1

Q4. Semiconductor Devices

a) In the diode application circuit shown below in Figure 3, the goal is to write an expression for V_out which depends on 3 distinct cases.

a. Case 1: V_in > V₁ + V_D

b. Case 2: (V₂ + V_D) < V_in < (V₁ + V_D)

c. Case 3: V_in < -(V₂ + V_D)

For a silicon PN junction bias voltage V_D = 0.7V, write an expression for V_out for each case.

Set the values of V1 and V2 to be the last two non-zero digits of your student ID.

Q5. Number Systems and Boolean Algebra

a) Assuming that your student ID number is a decimal number, convert it to Hexadecimal and BCD. Please show the workout.

[My student ID is 7546211].