Concept explainers
Using nodal analysis, find io(t) in the circuit in Fig. 10.60.
Figure 10.60
For Prob. 10.11.
Find the current
Answer to Problem 11P
The value of current
Explanation of Solution
Given data:
Refer Figure 10.60 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
Convert
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 current law at node
Simplify the equation as follows.
Apply Kirchhoff’s current law at node
MATLAB Code:
Solve the two linear equations (5) and (6) using MATLAB to find the node voltages.
syms v1 v2
eq1 = (0.5 + 0.5*1i)*v1 +(0.5*1i)*v2 == 3.464 + 2*1i;
eq2 = (0.5*1i)*v1 +(-1*1i)*v2 == 3 + (-3.464*1i);
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 + (%.3f)i V', v1real, v1imag)
v2=sprintf('%.3f + (%.3f)i V', v2real, v2imag)
The command window output:
v1 = '3.302 + (-4.417)i V'
From Figure 1, write the expression for
Substitute
Represent the current in time domain.
Conclusion:
Therefore, the value of current
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