# 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.

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#### 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.