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Q.

An ac source is initially connected to a resistor ‘R’ 
Situation (1) : If an inductor is connected in series with the resistor, the impedance in the circuit is 3R
Situation(2): If a capacitor is connected in series with resistor, the impedance in the circuit is 2R
Situation(3): Both the inductor and the capacitor are connected in series to the resistor.
In situation 3, if the phase of current and potential difference across the source is ϕ then |cotϕ|=pπ where p is nearly ________
 

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answer is 1.

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Detailed Solution

Situation (1) z2=R2+XL2XL=2R

Situation (2) z2=R2+XC2XC=3R

Situation (3) z2=R2+(XLXC)2z=626R & tanφ=XLXCR=23

cotφ=123|cotφ|=3+2=3.14 

p=1

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