wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

A capacitor is formed by two square metal plates of edge 1 m, separated by a distance 1 mm. Dielectrics of dielectric constant K1 and K2 are filled in the gap as shown in figure. The new capacitance is


[ Take ln2=0.7 ]

A
25 nF
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
10 nF
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
20 nF
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
15 nF
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A 25 nF

Let us consider a small strip of width dx at x distance from the left end.

From figure,

tanϕ=1×1031=1×103

t=xtanϕ=103x

We can see that both small capacitors formed by the small strip are in series.

So, 1dCeq=1dC1+1dC2

1dCeq=d1K1ϵ0A1+d2K2ϵ0A2

[ Area of small plate =1×dx=dx]

1dCeq=103103x2ϵ0dx+103x4ϵ0dx

dCeq=4ϵ0dx2×103103x

Ceq=dCeq=4ϵ010310dx2x

Ceq=4×8.85×1012103[ln(2x)]10[dxx=lnx+C]

Ceq=3.6×108[ln1+ln2]

Ceq=2.5×108 F=25 nF

Hence, option (d) is correct.

Why this question ?Tip-we use concept of integration for suchkind of problem. This question helps youto recall your concept of integration.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon