A linear resistive circuit has two inputs Vs1 and is2 with

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A linear resistive circuit has two inputs V_s1 and i_s2 with output Vout, as shown below. Table below shows the result of two sets of measurement taken in laboratory. Find the output voltage when the inputs are V_s1 = 10V and i_s2 = 8A.

1. 30V
2. -30V
3. 12V
4. None of these

Correct Option: A

From the linearity relation and from the given circuit

V_out = AV_s1 + Bi_s2 ⇒ (A) for appropriate A and B. The data from table imply that
3 = A × 5 + B × 0, which gives A = 0·6
Here A is dimensionless because V_out and V_s1 are both voltages.
Also, 6 = A × 0 + B × 2, which gives B = 3Ω
Here B has the unit of ohm. Therefore, the linear equation relating V_s1 and i _s2 to V_out is
V_out = 0·6V_s1 + 3i_s2
Now, when V_s1 = 10V and i_s2 = 8A then
V_out = 0·6 × 10 + 3 × 8 = 30V.