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amperes angular frequency applied average value behaviour branch capacitor voltage charge circuit current circuit theory complete component conductor coulombs current r.m.s. cycles per second damping determine device differential equation disc displacement dq/dt electrical equivalent series resistance evaluate example expression farads flux follows function given impedance induced e.m.f. inductive and capacitive inductive reactance inductor input current input voltage instant instantaneous joules lamp magnitude mathematical matrix mechanical system non-linear resistor notation ohms oscillation output voltage parallel particular phase angle potential difference power dissipated quantities r.m.s. value rate of change relationship represented resistive circuit rotating series circuit shaft shown in Figure simple harmonic motion simultaneous equations sine waves solution Suppose torque torsional pendulum value of current value of resistance vary sinusoidally vector of reference Vm sin cot voltage and current voltage equation voltage wave volts watts waveform waveshapes zero