
Reactance(X) and Resonance In an a.c circuit
Physics
Chima Sunday (Tutor)
16022016 14:19:00 +0000The opposition to current flow due to resistor presence in a circuit is called Resistance. When inductor or capacitor is present in a circuit the opposition it offers (i.e capacitor or inductor) is what we call Reactance. Consequenty, we have Capacitive Reactance which is the opposition to current flow due to capacitor in an a.c circuit. it is represented thus (X_{c} = ^{1}/_{2πfc}), where c = capacitor measured in Farad(F) and f = frequency measured in Hetz(Hz). And Inductive Reactance which is also an opposition to current flow when an inductor is present in an a.c circuit. It is reresented thus (X_{L} = 2πfl), where f = frequency measured in Hetz and l = inductor measured in Henry(H). Since both X_{L} and X_{c} opposes current flow, there units are still in respect of George Ohms(i.e Ohms)
So in a typical question where you are ask to find Capacitive reactance X_{c} when f and c are given. Also same for Inductive Reactance X_{L}, when f and l are given. As we will see in the following examples
(1)An inductor of 0.012H is connected to an a.c circuit of frequency 140Htz. Calculate the reactance of the inductor. (π = 22/7)
SOLUTION
recall that reactance of the inductor = X_{L} = 2πfl
here l = 0.012H, and f = 140Hetz
so X_{L} = 2×22/7 × 0.012 × 140 = 10.6 ohms
can you?
(1)In Nigeria, a.c supply is in frequency of 50Htz, if this same inductor above is connected to an a.c circuit of Nigeria kind frequency, Can you calculate the reactance of the inductor?
(2)What of if the same circuit is connected to a capacitor of 8 micro Farad. Can you calculate the reactance of the capacitor?

Lisa Elenya
question 1 xl=2πfl here l=?,and f=50Htz so xl=2×22/7×50=314.28 or314.3 question 2, 314.23×8=2514.24 or 2514.4
0 17022016 11:01:00 +0000

Chima Sunday (Tutor)
Always note the important of unit in any given physical quantity. So your answers lack unit. Can you see that? @Lily check Olamide work i think he is close to the answer, just that no unit to his answer.
0 17022016 11:46:00 +0000

beauty 09091645172
XL=2πfl. = 2*22/7*50*0.012 = 3.77 = 3.8. xc=2πfc = 2*22/7*50*8 = 2514.28 = 2514.3
0 18022016 09:18:00 +0000

Chima Sunday (Tutor)
No no no! @Beauty, you are right at inductor reactance, but at capacitive reactance you are not. please check our discussion above for a correct formula. @Fidelis, When a conductor opposes current flow we refer to it as resistance and not reactance. Although a conductor carrying current generates a varying electric field E, and from the theory of a Scottish physicist James Clerk Maxwell a varying Electric field E produce Magnetic field B, so we should also expect reactance. But they are negligible when compared with resistance. So we talk of the Resistance of a conductor to current flow and not its reactance. Please do feel free to relate back to me if you need more explanations. Thanks
0 18022016 09:46:00 +0000

Charles Omoregie
xc=1/2pilefc=2×22/7×50×8=0.00040 ohms xl=2pilefl=2×22/7×50×0.012=3.8 ohms
0 18022016 17:50:00 +0000

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