Solve the circuit in Fig. 10.5-9(a) for the current through the switch as a function of time.
SOLUTION
In this example, the two meshes in the circuit interact after t 0. We can solve this circuit
in many ways – branch-current method, mesh analysis, Thevenin’s equivalent, etc., are
some possibilities. First, we solve it by branch-current method.
Various branch currents in the circuit are identified in Fig. 10.5-9(b). We have to
get a differential equation in the current variable i.
Applying KCL at the switch node gives us i
2
i
1
– i.
Applying KVL in the first mesh gives us 15 10(i
1
i) ⇒i
1
1.5 – i
∴ i
2
1.5 – i– i 1.5 – 2i
Applying KVL in the second ...
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