Concept explainers
Use nodal analysis to find vo in the circuit of Fig. 10.58.
Figure 10.58
Find the voltage
Answer to Problem 9P
The value of voltage
Explanation of Solution
Given data:
Refer Figure 10.58 in the textbook for nodal analysis.
Formula used:
Write the expression to calculate impedance of the inductor.
Here,
Write the expression to calculate impedance of the capacitor.
Here,
Write the general representation of sinusoidal function.
Here,
Write the general expression to phasor transform of sinusoidal function from time domain to frequency domain.
Here,
Write the polar form representation of frequency domain.
Calculation:
Comparing given source voltage
Substitute
Substitute
Substitute
The frequency domain representation of given figure with the representation of node voltage is shown in Figure 1.
Apply Kirchhoff’s current law at node
Simplify the equation as follows.
Apply Kirchhoff’s current law at node
From Figure 1, write the expression for current
Substitute equation (7) in (6).
Simplify the equation as follows.
MATLAB Code:
Solve the two linear equations (5) and (8) using MATLAB to find the node voltage.
syms v1 v2
eq1 = (2 + 1*1i)*v1 +(-1*1i)*v2 == 10;
eq2 = (4 +(-1*1i))*v1 +(0.6 + 0.8*1i)*v2 == 0;
sol = solve([eq1, eq2], [v1, v2]);
val1 = sol.v1;
val2 = sol.v2;
v1real=real(val1);
v1imag=imag(val1);
v2real=real(val2);
v2imag=imag(val2);
v1=sprintf('%.3f + %.3fi V', v1real, v1imag);
v2=sprintf('%.3f + %.3fi V', v2real, v2imag)
The command window output:
v2 = '0.149 + 6.485i V'
From Figure 1, write the expression for
Substitute
Represent the voltage in time domain.
Conclusion:
Therefore, the value of voltage
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Chapter 10 Solutions
Fundamentals of Electric Circuits