Q6 of 805 Page 1

(a) An alternating voltage E = Eo sinωt is applied to a circuit containing a resistor R connected in series with a black box. The current in the circuit is found to be I = Io sin (ωt + π/4).


(i) State whether the element in the black box is a capacitor or inductor.


(ii) Draw the corresponding phasor diagram and find the impedance in terms of R.

(i) Given that E = E0Sin(ωt)


I = I0Sin(ωt + π/4)


It can be seen from the above two equations that phase angle of current at any point is greater than that of voltage by an amount of π/4. This means current leads the voltage in the circuit. This happens in a capacitive circuit. Therefore the element in the black box is a capacitor.


(ii)




Vc = VR


Xc = R


Impedance Z =


Z = R√2


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