A resistance less ring has 2 bulbs A & B rated at 2 V , 10 W and 2 V , 20 W respectively. The ring encloses an ideal solenoid whose magnetic field is as shown. The radius of solenoid is 1 m and the nu

Question

A resistance less ring has 2 bulbs A & B rated at $2 V, 10 W$ and $2 V, 20 W$ respectively. The ring encloses an ideal solenoid whose magnetic field is as shown. The radius of solenoid is 1 m and the number of turns/length $= 1000/ m$ . The current changes at rate of $9 A / sec$ . Find the power dissipated in bulb B in micro-Watt. $(π^{2} = 10)$

TestHub · Accepted Answer

R A ​ = P A ​ V 2 ​ = 10 4 ​ = 0.4 Ω ; R B ​ = 20 4 ​ = 0.2 Ω ε = ​ d t d ϕ ​ ​ = μ 0 ​ n A d t d i ​ = 4 π × 1 0 − 7 × 1000 × π ( 1 ) 2 × 9 = 36 π 2 × 1 0 − 4 = 0.036 V (π² = 10) Power dissipated in bulb B: P = ( R A ​ + R B ​ ε ​ ) 2 R B ​ = ( 0.6 0.036 ​ ) 2 × 0.2 = 7.2 × 1 0 − 4 W = 720 μ W

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