A person is riding a cycle at a speed of 18 km/hr along the equator. The wheel consists of 118 spokes and has a diameter of 50 cm . A bulb is attached between centre of wheel and its periphery. If the resistance of bulb is 0.3 uohm , then power dissipated in the bulb will be( given B earth = 25uT and assume no slipping)
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Given: A person is riding a cycle at a speed of 18 km/h along the equator. The wheel consists of 118 spokes and diameter of 50 cm. A bulb is attached between centre of wheel and its periphery. Resistance of bulb is 0.3 uohm
To find: Power dissipated in the bulb
Explanation: Velocity of cycle= 18 km/h = 18* (5/18)
= 5 m/s
Number of spokes= 118
Diameter(d)= 50 cm,
Radius(l) = d/2 = 25 cm
= 0.25 m
Magnetic field strength (B)= 25 uT
= 25 * 10^-6 T
Resistance(R) = 0.3 uohm = 0.3* 10^-6 ohm
Potential developed because of magnetic field strength(V)= B * v * l
= 25 * 10^-6 * 5 * 0.25
= 31.25 * 10^-6 m/s
Power dissipated across bulb
= V^2/R
= (31.25* 10^-6)^2/0.3* 10^-6
= 976.56 * 10^-12 / 0.3 * 10^-6
= 3255.2 * 10^-6 W
Therefore, the power dissipated across bulb would be 3255.2 * 10^-6 W.