A motor has coils with a resistance of 26 Ω and operates from a voltage of 244 V. When the motor is operating at its maximum speed, the back emf is 146 V. 

(a) Find the current in the coils when the motor is first turned on. 

 (b) Find the current in the coils when the motor has reached maximum speed. 

 (c) If the current in the motor were 7.0 A at some instant, what is the back emf at that time? 

A series RL circuit is built with 190 Ω resistor and a 5.0-cm-long, 1.0-cm-diameter solenoid with 800 turns of wire.

A) What is the peak magnetic flux through the solenoid if the circuit is driven by a 12 V, 5.0 kHz source?

B) What capacitance, in μF, has its potential difference increasing at 1.5×10⁶ V/s when the displacement current in the capacitor is 0.60 A ?

Consider a simple RL circuit consisting of an ideal battery with voltage 30 V , a resistor of resistance 15 Ω, an inductor of inductance 7.0 H, and a switch all in series. The switch is initially open. a) Determine the ratio of the voltage across the resistor to the voltage across the inductor when the current has a value of 1.5 A. b) How much time has elapsed if the voltage across the resistor is 20 V ?

The volume of a microbial culture increases according to the formula:

V (cm^3) = 5 - 0.2 t e^t

Where t is the time in seconds. It is requested:

a. The units of the constants 5 and 0.2

b. Calculate the expression for V (in^3) in terms of t (h).

c. The exponential function and its argument must be non-dimensional. In appearance, the given function contradicts two rules and, however, is valid. Explain the paradox.

A quality control engineer wishes to estimate the mean output voltage of a DC power supply for different loads. The engineer measures output voltage when the supply is connected to 11 different loads and computes a mean 98.4 V and standard deviation 7 V. Assume that the output voltages follow a normal distribution.

(a) Construct and interpret the 99.9% confidence interval.

(b) Construct and interpret the 90% prediction interval.

A particle moves along a straight line with an acceleration a=2v1/2m/s2, where v is in m/s.

If s = 0, v = 1 m/s when t = 0, determine the time for the particle to achieve a velocity of 18 m/s. Also, find the displacement of particle when t = 1 s. Express your answer using three significant figures and include the appropriate units.

A mass M travels at a speed V in the forward x- direction: It explodes into two pieces: one with mass m1 the other with mass m2. The mass m1 moves at an angle φ1 above the x-axis and the mass m2 moves at an angle φ2 below the x-axis. Both angles are directed in the forward direction. Find the magnitues of the momenta of the two pieces in terms of M V and the two angles

The velocity function for a particle moving along a straight line is given by v(t) = 2 − 0.3t for 0 ≤ t ≤ 10, where t is in seconds and v in meters/second. The particle starts at the origin.

(a) Find the position and acceleration functions for this particle.

(b) After ten seconds, how far is the particle from its starting point?

(c) What is the total distance travelled by the particle in the interval [0, 10]?