If the i-v characteristic for the electrical component C can be described by the

Question

If the i-v characteristic for the electrical component C can be described by the linear equation:

i = 0.27V - 0.02

Find the voltage, current and power for component C, given the following connections to terminals a and b. Also state whether component C is a source (supplying energy) or a load (dissipating energy).

a) An ideal current source is = 0.08 A is connected to the a-b terminals as shown.

v=? i=? power=?

b) A 55 resistor is connected to the a-b terminals as shown.
(hint: you must use the given equation i = 0.27*v - 0.02, and combine it with another equation to solve for v and i...)

v=? i=? power=?

Explanation / Answer

a) The first thing is to realize that in a loop, the same current MUST flow through all elements connected in that loop. There is no other branches for current to escape or flow in from. So therefore i, the current flowing into element c must be:
-is = i

using this relationship:

-0.08 = 0.27*V - 0.02 Amps

solving for V:

V = (-0.06/0.27) = -0.222 Volts

Now we know the power dissipated by the element C...

P = V * I = (-0.08 A)*(-0.222 V) = 0.01777 or 17.8 mW

B) looking at the nodes a to b. We see that the resistor and element C are in parallel. They thus share the same voltage. So the voltage of R is the voltage of C.

V = i*R where i is the equation (0.27*v - 0.02) and R is the resistor.

i = (0.27)*(55*i) - 0.02 = 14.85*i -0.02

subtracting 14.85i from both sides I get:

-13.85*i = -0.02

i = ( 0.02 / 13.85) = 1.444 mA

The power dissipated by resistor will equal the power dissipated by element C.

Power = I2*R = 0.1147 mW

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