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Homework Statement
The circuit shown has two inputs, [tex]V_{s}[/tex] and [tex]i_{s}[/tex] and one output [tex]V_{o}[/tex]. The output is related to the input by the equation [tex]V_{o}=ai_{s}+bV_{s}[/tex] where a and b are constants to be determined. determine the values a and b by (a) writing and solving mesh equations and (b) writing and solving node equations.
Homework Equations
Kirchoff's Voltage Law (Sum of voltages in a closed loop = 0)
Kirchoff's Current Law (Sum of currents at a node = 0)
Ohm's Law ([tex]V=IR[/tex])
The Attempt at a Solution
Loop 1 ([tex]i_{1}[/tex])
[tex]V+96(i_{1}i_{2})+120(i_{1}i_{3})=0[/tex]
Loop 2 ([tex]i_{2}[/tex])
[tex]96(i_{2}i_{1})+32i_{2}V_{s}=0[/tex]
Loop 3 ([tex]i_{3}[/tex])
[tex]120(i_{3}i_{2})+V_{s}+30i_{3}=0[/tex]
Constraint
[tex]i_{1} = i_{s}[/tex]
How am I to solve for anything? I have 5 equations and eight unknowns ([tex]V, V_{s}, i_{s}, i_{1}, i_{2}, i_{3}, a, b[/tex]). I know these equations are right because my professor helped the class set up all of the homework problems on Monday. I just don't know how to find V. Please help!
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