Circuit Analysis Problem

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Questions and Answers

What is the equation obtained by applying KVL for loop ABEFA?

-5I1 - 10 - 10(I1 - I2) + 30 = 0

-5I1 + 20 + 10(I1 - I2) - 40 = 0

-5I1 - 10 - 20(I1 - I2) + 20 = 0

-5I1 - 20 - 10(I1 - I2) + 40 = 0 (correct)

What is the equation obtained by multiplying equation (1) by 2 and equation (2) by 3?

-25I1 + 15I2 = -25, 25I1 - 30I2 = -30

-15I1 + 12I2 = -15, 18I1 - 22I2 = -18

-30I1 + 20I2 = -40, 30I1 - 36I2 = -30 (correct)

-20I1 + 10I2 = -20, 20I1 - 24I2 = -20

What is the value of I2 in amperes?

I2 = 5.125 Amp

I2 = 6.25 Amp

I2 = 4.375 Amp (correct)

I2 = 3.75 Amp

What is the SI unit of electric work?

Joule Signup and view all the answers

What is the method used to analyze the given circuit?

Mesh Analysis Signup and view all the answers

What is the rate at which electrical energy is transferred by an electric circuit?

Power Signup and view all the answers

What is the use of Cramer's Rule in circuit analysis?

To solve a system of linear equations Signup and view all the answers

What is the SI unit of power?

Watt Signup and view all the answers

What is the purpose of applying KVL for loop BCDEB?

To write another equation to solve for the currents Signup and view all the answers

What is the formula to calculate the resistance of a coil?

R = ρl / A Signup and view all the answers

What is the formula to calculate the current in a circuit?

I = V / R Signup and view all the answers

What is the formula to calculate the power absorbed by a coil?

P = V × I Signup and view all the answers

What is the total length of the coil?

160000 cm Signup and view all the answers

What is the resistance of the coil?

40 Ω Signup and view all the answers

What is the value of I1 when using Cramer's Rule?

4.25 Amp Signup and view all the answers

What is the value of total current through the 10 ohm resistor?

-0.125 Amp Signup and view all the answers

What is the value of VB in the given circuit?

-1.25V Signup and view all the answers

What is the value of ∆ in Cramer's Rule?

80 Signup and view all the answers

What is the value of I2 when using Cramer's Rule?

4.375 Amp Signup and view all the answers

What is the application of Node Analysis in this circuit?

To find the voltage at a node Signup and view all the answers

What is the value of I when using Mesh Analysis?

-0.125 Amp Signup and view all the answers

What is the value of ∆1 in Cramer's Rule?

340 Signup and view all the answers

What is the application of Cramer's Rule in this circuit?

To solve systems of linear equations Signup and view all the answers

What is the value of I1 + I2?

8.625 Amp Signup and view all the answers

Study Notes

KVL and Circuit Analysis

Applying Kirchhoff's Voltage Law (KVL) to loop ABEFA yields an equation describing voltage drops around the loop.
Simplify the equation: -15I1 + 10I2 = -20
Apply KVL to loop BCDEB: -2I2 + 10 - 10(I2 - I1) = 0
Simplify the equation: 10I1 - 12I2 = -10
Solve for I2 by multiplying equation (1) by 2 and equation (2) by 3, and then adding them: I2 = 4.375 Amp
Solve for I1 by substituting I2 in equation (1): I1 = 4.25 Amp

Electric Work and Power

Electric work: the work done per unit of charge
SI unit of electric work: Joule
Electric power: the rate at which electrical energy is transferred
SI unit of electric power: Watt (one Joule per second)

Coil Resistance and Power

Calculate the total length of the coil: ltotal = 160000 cm = 1600 m
Calculate the resistance of the coil: R = 40 Ω
Calculate the current: I = 2.75 Amp
Calculate the power absorbed by the coil: P = 302.5 Watt

Equivalent Resistance in Parallel Connection

Derive an expression for equivalent resistance: R_equivalent = (R1*R2)/(R1+R2)
Calculate the total current through the 10 ohm resistor: I = I1 - I2 = -0.125 Amp