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Q.

An inductance of 1mH, a condenser of 10μF and resistance of 50Ωare connected in series. The reactance of inductors and condensers are the same. The reactance of either will be:


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a

100Ω

b

30Ω

c


d

10Ω 

answer is D.

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Detailed Solution

Concept: Reactance is the resistance to current flow caused by the inductance or capacitance of a circuit element. For a given applied voltage, fewer currents result from greater reactance.
When alternating current circulates in a loop, the circuit resistance works against the current flow. Condenser and inductor are two other components that can be employed. Therefore, the movement of current is resisted by these components. Reactance is known to be an inductor and condenser's ability to oppose current flow. The reactance of a capacitor is known as capacitive reactance and is indicated by XC, whereas the reactance of an inductor is known as inductive reactance.
It is the size of the imaginary component of the mechanical or acoustic impedance. When there is a potential difference in an inductive reactance, the current across it changes. The relative potential difference and pace of present change Power does not diminish as a result of reaction. The inductive response for an inductor connected to the circuit along with the AC power source is given by the equation below.
XL=ωL
where L is the inductance, XL is the reactance, and is the angular frequency
As stated in the question, we now understand that the inductor's and condenser's reactances are identical.
Therefore,
ωL=1ωc
Now,
ω2=1LC
Now we have,
L=1mH OR 10-3H
C=10μF OR 10-5F
Now,
⇒ω=1/10-3×10-5
⇒ω=1/10-8
⇒ω=104
Now,
Using the Formula to Calculate Reactance
XL=ωL
⇒X
L=104×10-3
⇒X
L=10Ω
As a result, the inductor and condenser reactance is 10Ω.
Hence, the correct answer option (4) .
 
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