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An (open) electric circuit consists of an inductor, a resistor, and a capacitor. There is an initial charge of 2 coulombs on the capacitor. At the instant the circuit is closed, a current of 3 amperes is present and a voltage of E(t) = 20 cos t is applied. In this circuit the voltage drop across the resistor is 4 times the instantaneous change in the charge, the voltage drop across the capacitor is 10 times the charge, and the voltage drop across the inductor is 2 times the instantaneous change in the current. Write an initial value problem to model the circuit.

An (open) electric circuit consists of an inductor, a resistor, and a capacitor. There is an initial charge of 2 coulombs on the capacitor. At the instant the circuit is closed, a current of 3 amperes is present and a voltage of E(t) = 20 cos t is applied. In this circuit the voltage drop across the resistor is 4 times the instantaneous change in the charge, the voltage drop across the capacitor is 10 times the charge, and the voltage drop across the inductor is 2 times the instantaneous change in the current. Write an initial value problem to model the circuit.

Delmar's Standard Textbook Of Electricity
Delmar's Standard Textbook Of Electricity
7th Edition
ISBN:9781337900348
Author:Stephen L. Herman
Publisher:Stephen L. Herman
Chapter20: Capacitance In Ac Circuits
Section: Chapter Questions
Problem 7PP: A pure capacitive circuit is connected to a 480-volt, 60-Hz power source. An ammeter indicates a...
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An (open) electric circuit consists of an inductor, a resistor, and a
capacitor. There is an initial charge of 2 coulombs on the capacitor.
At the instant the circuit is closed, a current of 3 amperes is
present and a voltage of E(t) = 20 cos t is applied. In this circuit
the voltage drop across the resistor is 4 times the instantaneous
change in the charge, the voltage drop across the capacitor is
10 times the charge, and the voltage drop across the inductor
is 2 times the instantaneous change in the current. Write an initial
value problem to model the circuit.

Expert Solution
Step 1

Given that:

  • Initial charge q(0)=2 C
  • I=3 A
  • E(t)=20 cos(t)
  • The voltage drop across the resistor is 4 times the instantaneous change in the charge q.
  • The voltage drop across the capacitor is 10 times the charge.
  • The voltage drop across the inductor is 2 times the instantaneous change in the current.
  • Write the initial value problem of the circuit.
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