Exercises 5.6voltage source. We apply Kirchhof’s voltage law,EL+ER+EC=E(t), to Loop 1 andLoop 2 to get two equations connecting currents in the network. (Similarly to Example 2 andProblem 11, there is no need to apply Kirchhof’s voltage law to Loop 3 because the resultingequation is just a linear combination oF those For other two loops.)Loop 1:EL+ER=0⇒0.5dI1dt+1·I2⇒dI1dt+2I2.(5.37)Loop 2:EL+EC=cos3t⇒0.5dI1dt+q30.5t⇒dI1dt+4q3=2cos3t.(5.38)Additionally, at joint points, by Kirchhof’s current law,−I1+I2+I3⇒−I1+I2+dq3dt.(5.39)Putting (5.37)–(5.39) together yields the Following system:
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