1.

A short circuited coil is placed in a time varying magnetic field. Electrical power is dissipated in the form of Joule heat due to the current induced in the coil. If the number of turns were to be quadrupled and the wire radius halved, the electrical power dissipated would be .........

Answer»

halved
the same
doubled
quadrupled

Solution :LET `EPSILON=-N . (dphi)/(dt)`, here if `-(dphi)/(dt)` then `epsilon prop N` …(1)
and `R=(rhol)/A` is constant in `rho/pi`
`therefore R prop L/r^2` …(2)
And power `P=epsilon^2/R=(N^2r^2)/l`
`therefore P_1/P_2=(N_1/N_2)^2xx(r_1/r_2)^2xx(l_2/l_1)`...(3)
Now by constant volume , increasing the length of wire from `l_1` to `l_2` its radius BECOMES from `r_1` to `r_2`
`therefore pir_1^2l_1 = pir_2^2l^2`
`therefore (r_1/r_2)^2 =l_2/l_1`....(4)
From EQN. (3) and (4) ,
`therefore P_1/P_2=(N_1/N_2)^2xx(r_1/r_2)^4`...(5)
If `N_2=4N_1` and `r_2=r_1/2` then,
`P_1/P_2=(1/4)^2 xx(2)^4 =1:1`


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