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Mesh analysis techniques to determine currents

A. Using Maxwell's circulating currents, calculate the three complex currents. Assume an angular frequency of 2.2 Mhz.

b. Sketch a phasor diagram showing all the currents and the two voltages V1 and V2.

Please refer to the attachment for circuit diagram.


Solution Preview

a. First of all let us determine the impedances in complex form:

For the 9nF capacitor Z(cap)

Z(cap) = 1/{j x 2.2*w; x 10^6 x 9 x 10^-9} = -j16.1 = 16.1&Angle;arctan(-16.1/0) = 16.1Angle(-90)

For the resistor 12 Ohm; resistor Z(R)

Z(R) = 12 Ohm

For the 1.1 uH inductor Z(In)

Z(In) = j x 2.2pi x 10^6 x 1.1 x 10^-6 = j8.0 = 8Angle arctan(8/0) = 8Angle(90)

Note we have two loops; call them Loop one to the LHS of circuit diagram and Loop 2 to the RHS of the circuit diagram. We ignore current i2 for the moment and just consider the Maxwell circulating currents or Mesh currents.

For the 1st Maxwell current loop: (i.e. the current that flows in loop 1, i1 in circuit diagram)

i1*{Z(cap) + Z(R)} - i3*Z(R) = V1 -V2 (1)

For the 2nd Maxwell current loop: (i.e. the current that flows in loop 2, i3 in circuit diagram)

i3*{Z(R) + Z(In)} - i1*Z(R) = V2 (2)

Thus we have simultaneous equations (1) & (2) to solve.

Multiplying (1) by {Z(R) + Z(In)}we get

i1*{Z(cap) + Z(R)}*{Z(R) + ...

Solution Summary

An example of using mesh analysis to determine currents in a circuit. The expert sketches a phasor diagram showing the currents and two voltages.