Question

Find the the current I(t) in an LRC series circuit, using the given initial current and the charge on the capacitor, when L =0.02H, R =2ohms, c=0.001F, E(t)=150volts, Q(0)=5c and I(0)=0A. Please show each step with any explanation. Thanks

Answer 1

The input voltage at time t is given as

E(t) = 150 V

The total impedance Z can be found as,

Z = Z of Resistance, R + Z of Inductor, X_L + Z of capacitance, X_C

Since

•   The instantaneous voltage across a pure resistor, V_R is “in-phase” with current
•   The instantaneous voltage across a pure inductor, V_L “leads” the current by 90^o
•   The instantaneous voltage across a pure capacitor, V_C “lags” the current by 90^o

we cannot just add up the impedances, but only through analysing the phasor diagrams and all. After analysing the phasor diagram for instantaneous voltages and formulating equations for ohms law for individual components, finally we will yield the equation for total impedance, Z as

We know from ohms law that V = IZ

So I = V/Z

But we need to find X_L and X_C.

Hz

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