An ac source of angular frequency ω is fed across a resistor R and a capacitor C in series. The current registered isI . If now the frequency of source is changed to ω$$3$$ (but$$ maintaining the same $$voltage), the current in the circuit is found to be halved. Then the ratio of reactance to resistance at the original frequency ω is

Question

An  ac source of angular frequency ω      is fed across a  resistor R      and a capacitor C      in series. The  current registered isI     . If now the frequency of source is changed to ω$$3$$     (but$$ maintaining the same $$voltage), the current in the  circuit is found to be halved. Then the ratio of reactance to resistance at  the original frequency ω      is

Infinity Learn · Accepted Answer

According  to given problem,  $$I=VZ=V$$[$$R2+(1C$$ω$$)2$$]$$12$$                        ……..(1)and$$ $$I2=V$$[$$R2+(3C$$ω$$)2$$]$$12$$                    ……..$$(2)substituting$$ the value of I from  eq.$$(1) in (2),$$4(R2+1C2$$ω$$2)=R2+9C2$$ω$$2$$     i.e.,$$1C2$$ω$$2=35R2$$     So that $$XR=(1C$$ω$$)R=(35R2)12R=35$$     .

Start JEE / NEET / Foundation preparation at rupees 99/day !!

Detailed Solution

Get Expert Academic Guidance – Connect with a Counselor Today!