A series RLC circuit with R = 6 ohm, C = 0.02 Farad and L = 0.1 has no applied voltage. Find the subsequent current in the circuit if the initial charge, on the capacitor is q0 and the initial current is zero.
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Expert's answer
2020-04-02T13:43:13-0400
A series RLC circuit with R=6 ohm, C=0.02 Farad and L=0.1 has no applied voltage. Find the subsequent current in the circuit if the initial charge, on the capacitor is q0 and the initial current is zero.
Kirchhoff's voltage law:
uR+uL+uC=0
where uR,uL,uC are the voltages across R,L and C respectively.
Substituting in the constitutive equations:
Ri(t)+Ldtdi(t)+C1−∞∫ti(τ)dτ=0
Differentiating and dividing by L :
dt2d2i(t)+LRdtdi(t)+LC1i(t)=0
This can usefully be expressed in a more generally applicable form:
dt2d2i(t)+2αdtdi(t)+ω02i(t)=0α=2LR,ω0=LC1
The differential equation has the characteristic equation:
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