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Alternating Current Circuits

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Question
ICSEENIPH12029755
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Alternating current flowing through a certain electrical device leads over the potential difference across it by 90° State whether this device is a resistor, capacitor or an inductor.

Solution

Capacitor

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Question
ICSEENIPH12029775
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(i) Figure 6 below shows a series RCL circuit connected to an ac source which generates an alternating emf of frequency 50 Hz. The readings of the voltmeters V1 and V2 are 80 V and 60 V respectively.

Find :

(1)    The current in the circuit.

(2)    The capacitance C of the capacitor.

(ii) At resonance what is the relation between impedance of a series LCR circuit and its resistance R?

Solution

(i)
V1 = 80V

Current in circuit, I = fraction numerator straight V apostrophe over denominator straight R end fraction space equals space 80 over 100 space equals space 0.8 space A
Capacitance is given by, 
straight chi subscript straight C space equals space 1 over ωC space equals space straight V squared over straight I space equals space fraction numerator 60 over denominator space 0.8 end fraction straight i. straight e. comma space fraction numerator 60 over denominator 0.8 end fraction space equals space 1 over ωC rightwards double arrow space straight C space equals space fraction numerator 0.8 over denominator 60 space straight x space straight omega end fraction space equals space fraction numerator 0.8 over denominator 60 space straight x space 2 straight pi space straight x space 50 end fraction space space space space space space space space space equals space 42.4 space μF  

ii )
At resonance,
straight chi subscript straight C space equals space straight chi subscript straight L So comma space Impedence space equals space straight R straight Z space equals space square root of straight R squared plus left parenthesis straight chi subscript straight L minus straight chi subscript straight C right parenthesis squared end root space equals space straight R space 

Question
ICSEENIPH12029796
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Which one of the following graphs in represents variation of reactance ‘XC’ of a capacitor with frequency ‘f ’ of an AC supply:

Solution

D.

Question
ICSEENIPH12029803
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Variation of alternating current T with time ‘t’ is shown in the graph below :




What is the rms value of this current?

Solution

 I subscript r m s end subscript space equals fraction numerator straight I subscript max over denominator square root of 2 end fraction F r o m space t h e space c u r v e comma space I subscript m a x end subscript space equals space 5 square root of 2 equals fraction numerator 5 square root of 2 over denominator square root of 2 end fraction equals 5 A

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