The lightbulb in the circuit shown in the figure has a resistance of 14 Ω and consumes 4.2 W of power; the rod is 1.18 m long and moves to the left with a constant speed of 2.9 m/s . The strength of the magnetic field is 2.2 T .
Find the current that flows in the circuit.
What speed must the rod have if the current in the circuit is to be 1.3 A?
To find the current that flows in the circuit, we can use the formula for power:
Power (P) = Current (I) * Voltage (V)
Since the resistance (R) of the lightbulb is given, we can calculate the voltage using Ohm's Law:
Voltage (V) = Current (I) * Resistance (R)
Given that the power is 4.2W and the resistance is 14Ω:
I * V = 4.2W
I * (I * R) = 4.2W
I^2 * R = 4.2W
I^2 * 14Ω = 4.2W
I^2 = 4.2W / 14Ω
I^2 = 0.3A^2
Taking the square root of both sides:
I = sqrt(0.3A^2)
I ≈ 0.55 A
Thus, the current that flows in the circuit is approximately 0.55 A.
To find the speed at which the rod must move in order to have a current of 1.3 A, we can use the formula for the emf induced in a moving rod in a magnetic field:
emf = (B * L * v)
Where:
B is the strength of the magnetic field (given as 2.2 T)
L is the length of the rod (given as 1.18 m)
v is the speed of the rod
Since the emf is directly proportional to the speed, we can set up a proportion:
emf1 / v1 = emf2 / v2
Given that the current (I) is related to the emf, we can use Ohm's Law:
emf = I * R
Where:
I is the desired current (given as 1.3 A)
R is the resistance (given as 14 Ω)
Plugging in the values:
I * R = (B * L * v)
1.3 A * 14 Ω = (2.2 T * 1.18 m * v)
18.2 V = (2.596 m^2 * v)
v ≈ 7.02 m/s
Thus, the speed at which the rod must move in order to have a current of 1.3 A is approximately 7.02 m/s.