SET UP AND SOLVE To find the emf, we use = vBL: Let us apply the concepts of mot
ID: 1774830 • Letter: S
Question
SET UP AND SOLVE To find the emf, we use = vBL: Let us apply the concepts of motional emf and Lenz's law toa slide-wire generator. Suppose the length L of the slide-wire rod in (Fiqure 1) is 0.10 m, its speed v is 2.5 m/s, the total resistance of the loop is 0.030 2, and B is 0.60 T. Find the emt, the induced current, the force acting on the rod, and the mechanical power needed to keep the rod moving at constant speed. -uBL = (2.5m/s)(0.60T)(0.10m) = 0.15V From Ohm's law, the current in the loop is 1-E/R = (0.15V)/(0.03012) = 5.0A Lenz's law tells us that an induced force acts on the rod, opposite to the rod's direction of motion. The magnitude of this force is Ftndlined 1 LB = (5.0A )(0.10m)(0.60T) = 0.30N To keep the rod moving at constant speed, a force equal in magnitude and opposite in direction to indced must act on the rod. Therefore, the mechanical power P P dced (0.30N) (2.5m/s) 0.75W needed to keep the rod moving is REFLECT The expression for the emf is the same result we found from Faraday's law. The rate at which the induced emf delivers electrical energy lo the circuit is P = -(0.15V) (5.0A) = 0.75W This is equal to the mechanical power input, I as we should expect. The system is converting mechanical energy (work) into electrical energy. Finally, the rate of dissipation of electrical energy in the circuit resistance is P-T2 R = (5.0A )2 (0.03(n) = 0.75W which is also to be expected. Part A Practice Problem: 3.0m/ s the total resistance of the loop is 0 075Q, and B = 0.60T find the rate at which the induced emf delivers electrial energy to lf = 0.20m the circuit u Express your answer to two significant figures and include appropriate units. ValueUnitsExplanation / Answer
P = EI = (vBL)(vBL/R) = (vBL)2/R = (3 x 0.6 x 0.2)2/0.075 = 1.728 W
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.