Suppose a linear circuit contains a voltage source and a current source. When th

Question

Suppose a linear circuit contains a voltage source and a current source. When the voltage source is set to 10V and the current source is set to 10 mA, the output voltage is 1V. When the voltage source is set to 10V and the current source is set to 0 mA, the output voltage is 2V. Show mathematically what the output voltage would be if the voltage source is set to 5V and the current source is set to 20 mA.

Explanation / Answer

Since the circuit is linear, the output voltage will be a linear combination from the voltage source and current source values: Vout = aV + bI for V=10 and I = 10 we have: Vout = 1 -> 10a+10b = 1 for V=10 and I = 0 we have: Vout = 2 -> 10a+0 = 2 Solving this system of equations we have: a = 0.2 , b = -0.1 Therefore: Vout = 0.2V - 0.1I and for V=5 , I=20 , we have: Vout = 0.2*5 - 0.1*20 = 1-2 = -1 V

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