Concept explainers
Use mesh analysis to find vo in the circuit of Fig. 10.78. Let vs1 = 120 cos (100t + 90°) V, vs2 = 80 cos 100/ V.
Figure 10.78
Find the voltage
Answer to Problem 30P
The value of voltage
Explanation of Solution
Given data:
Refer Figure 10.78 in the textbook for mesh 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
Comparing given source voltage
Substitute
Substitute
Substitute
Substitute
Substitute
The frequency domain representation of given figure with the representation of node voltage is shown in Figure 1.
Apply Kirchhoff’s voltage law in the loop with current
Apply Kirchhoff’s voltage law in the loop with current
Apply Kirchhoff’s voltage law in the loop with current
MATLAB Code:
Solve the linear equations (5), (6) and (7) using MATLAB to find the mesh currents.
syms i1 i2 i3
eq1 = (2 + 3*1i)*i1 -3*1i*i2 +0*i3 == 12*1i;
eq2 = -3*i1 -13*i2 +20*i3 == 0;
eq3 = 0*i1 +20*1i*i2 +(1-18*1i)*i3 == -8;
sol = solve([eq1, eq2, eq3], [i1, i2, i3]);
val1 = sol.i1;
val2 = sol.i2;
val3 = sol.i3;
i1real=real(val1);
i1imag=imag(val1);
i2real=real(val2);
i2imag=imag(val2);
i3real=real(val3);
i3imag=imag(val3);
i1=sprintf('%.3f + %.3fi A', i1real, i1imag)
i2=sprintf('%.3f + %.3fi A', i2real, i2imag)
i3=sprintf('%.3f + %.3fi A', i3real, i3imag)
The command window output:
i1 = '2.0557 + 3.5651i A'
i2 = '0.4324 + 2.1946i A'
i3 = '0.5894 + 1.9612i A'
From Figure 1, write the expression for
Substitute
Represent the voltage in time domain.
Conclusion:
Therefore, the value of voltage
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