CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

A coil of inductance L and resistance r is connected in series with a 4 $$\Omega$$ resistor to a battery of emf E volt through a switch S. The switch S is closed at time $$\mathrm{t}=0  \mathrm{s}$$ and the potential dlfference across the inductor $$(V_{ab})$$  is measured and its variation in time t is shown in the above graph. FInd the resistance of the coil (in $$\Omega$$).

44592_59117631b06b40b98a331f7dae990db7.png


A
1Ω
loader
B
1.2Ω
loader
C
4Ω
loader
D
2Ω
loader

Solution

The correct option is A $$1\Omega$$
At $$t=0$$s, due to induction, L behaves as an open circuit, current in the circuit is zero.
$$\therefore V_{ab} = E =10V,$$ from the graph
After long time, steady current $$I_{0}$$ is established, the coil behaves like a resistor of resistance r.
As$$t\rightarrow \infty ,V_{ab}=2.0=I_{0}r$$
Now, Applying KVL
$$\therefore E-4I_{0}-I_{0}r=0$$
i.e.$$10-4I_{0}-2=0$$
or$$I_{0}=2A$$

Now $$r=\displaystyle \dfrac{2}{I_{0}}=\dfrac{2}{2}=1\Omega $$

Physics
NCERT
Standard XII

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
Same exercise questions
View More


similar_icon
People also searched for
View More



footer-image