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

Obtain an expression for e.m.f. induced in a coil rotating with uniform angular velocity in a uniform magnetic field. Show graphically the variation of e.m.f. with time (t).
Resistance of a potentiometer wire is 0.1Ω/cm. A cell of e.m.f. 1.5V is balanced at 300cm on this potentiometer wire. Calculate the current and balancing length for another cell of e.m.f. 1.4V on the same potentiometer wire.

Open in App
Solution

When a rectangular coil EFGH is rotated about its axis in plane perpendicular to the plane of a field, then the magnetic flux B passing through the coil changes, as a result an induced e.m.f. gets developed.
Consider a coil which has area A=lb and n be the number of turns of the coil. It is being rolled in a uniform magnetic field (B) with an uniform angular velocity ω. At any instant of time, the angle between the normal of the coil and that of field of B, then the flux associated with the coil is
ϕ=nBAcosθ ...(i)
The plane of the coil is perpendicular to the magnetic field then after time t, is rotated by angle θ.
Hence, ω=θt or θ=ωt
by equation (i) ϕ=nBAcosωt ...(ii)
By Faraday's law
E=dϕdt=ddt (nBAcosωt)
E=nBAωsinωt
The graph showing the variation with time 't' of the e.m.f. induced in the coil.
R=0.1Ω/cm, V2=1.4V
L1=300cm I2=?
V1=1.5V, L2=?
Current :
I1=V2R=1.40.1=14A
Balancing length,
K=V1L1=1.5300=5×103V/cm
L2=V2K=1.45×103=280cm.

628358_601193_ans.png

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Electrical Instruments
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon