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Unformatted text preview: The RLC Circuit The RLC circuit is the electrical circuit consisting of a resistor of resistance R , a coil of inductance L , a capacitor of capacitance C and a voltage source arranged in series. If the charge C R L V on the capacitor is Q and the current flowing in the circuit is I , the voltage across R, L and C are RI, L dI dt and Q C respectively. By the Kirchhoff’s law that says that the voltage between any two points has to be independent of the path used to travel between the two points, LI ( t ) + RI ( t ) + 1 C Q ( t ) = V ( t ) Assuming that R, L, C and V are known, this is still one differential equation in two unknowns, I and Q . However the two unknowns are related by I ( t ) = dQ dt ( t ) so that LQ 00 ( t ) + RQ ( t ) + 1 C Q ( t ) = V ( t ) or, differentiating with respect to t and then subbing in dQ dt ( t ) = I ( t ), LI 00 ( t ) + RI ( t ) + 1 C I ( t ) = V ( t ) For an ac voltage source, choosing the origin of time so that V (0) = 0, V ( t ) = E sin( ωt ) and the...
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- Fall '10