Question

Suppose a circuit has a resistor, capacitor and voltage source connected in series. The resistance is R = 20ohms, the capacitance is C = 3 farads and the voltage source has a constant voltage of 70 volts.

a) Let q(t) be the charge (in coulombs) on the capacitor after t seconds. Write a differential equation in termsof q(t)

Answer 1

The differential equation for the charge on the capacitor is q'(t) = (E - IR) * C.

Step-by-step explanation:

The charge on the capacitor can be given by the equation Q(t) = C * Vc(t), where C is the capacitance and Vc(t) is the voltage across the capacitor at time t. In this case, the voltage across the capacitor can be obtained using Ohm's law and Kirchhoff's loop rule, Vc = (E - VR), where E is the constant voltage of the source and VR is the potential drop across the resistor. The potential drop across the resistor can be represented as VR = IR, where I is the current flowing through the circuit.

Substituting these equations into the original equation, we get the differential equation in terms of q(t):

q'(t) = (E - IR) * C