(a) The schematic sketch of a cyclotron is drawn here. The positively charged particle produced at the centre of cyclotron is attracted towards the dee (say `D_(1)`) which is at a negative potential at that time. The charged particle acquires some velocity (say `v_(1)`) due to attraction of electric field. But once the charged particle enters into the dee, it describes a circular path of radius `r_(1)=(mv_(1))/(qB)`.
After describing a semicircular path inside dee `D_(1)`, the particle comes in the gap between the two dees. In the resonance condition, the direction of electric field just gets reversed during this time and particle is again accelerated towards the dee `D_(2)` and its velocity `v_(2)` becomes greater. So, the charged particle describes a semicircular path in dee `D_(2)` whose radius `r_(2)=(mv_(2))/(qB)` is slightly greater than `r_(1)` As time taken by charged particle to cover the semicircular path remains unchanged, same thing happens again and again and particle describes semicircular paths of gradually increasing radii in dees `D_(1)` and `D_(2)` again and again.
(b) Let us have a galvanometer of resistance `R_(G)` and giving full scale deflection for a current `I_(g)` to convert it into a voltmeter of ranges 2V,V and `V/2` respectively, we are joining resistances `R_(1),R_(2)` and `R_(3)` so we have
`R_(1)=(2V)/(I_(g))-R_(g)` ...(i)
`R_(2)=V/(I_(g))-R_(g)` ....(ii)
and `R_(3)=(v//2)/(I_(g))-R_(g)` ....(iii)
On solving these equations, we get
`R_(1)-R_(2)=2R_(3)` or `R_(1)=R_(2)+2R_(3)`
