Two tangent galvanometers A and B have coils of radii `8cm` and `16cm` respectively and resistance 8`Omega` each. They are connected in parallel to a cell of emf `4V` and negligible internal resistance. The deflections produced are `30^@` and `60^@` respectivley. A has 2 turns. What is the number of turns in B?

Options

A. 18 turns
B. 12 turns
C. 6 turns
D. 2 turns

Answer

B

Explanation

Current in tangent galvonometer
`" " l=(2rH)/(mu_(0)N) tan theta`

`Here, `R_(1) and R_(2) "are in parallel"`
`therefore " " (1)/(R_("net"))=(1)/(R_(1))+(1)/(R_(2))=(R_(1)+R_(1))/(R_(1)R_(2))=(8+8)/(8xx8)`
`" " R_("net")=4Omega`
`Hence, l=(V)/(R)=(4)/(4)=1A`
From eq. (i), we get
`" " (r tan theta)/(N)=(mu_(0)I)/(2H)`
`" " (r_(A) tan theta_(A))/(N_(A))=(r_(B) tan theta_(B))/(N_(B))`
`Rightarrow " " (8xx1)/(sqrt3xx2)=(16xxsqrt3)/(N_(B))`
`therefore " " N_(B)=12 turns`