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6. Derive a power balance equation for the RL and RC circuits. (see Problem 5) Discuss the significance of the signs of the three power terms.
5. The power generated or dissipated by a circuit element equals the voltage across the element times the current through the element. Show that the power dissipated by a resistor equals
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Fundamentals of Differential Equations and Boundary Value Problems
- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.arrow_forward1. Suppose that the dependent variable y is directly related to the independent variable x by the equation y=1.5 + 2x. a. Find the value of y that corresponds to'x -1. b. Find the value of y that corresponds to x = 3. c. Graphs and equations have an important relationship. All the points that satisfy the equation y = 1.5+ 2x have a common property. What is it?arrow_forward12. The amount of heat H (in joules) required to convert one gram of water into vapor is linearly related to thetemperature T (in ?? ) of the atmosphere. At 10?? this conversion requires 2480 joules, and each increasein temperature of 15?? lowers the amount of heat needed by 40 joules. Express H in term of T.arrow_forward
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- 2. Thermistors measure temperature, have a nonlinear output and are valued for a limited range. So when a thermistor is manufactured, the manufacturer supplies a resistance vs. temperature curve. An accurate representation of the curve is generally given by = a₁ + a₂ ln(R) + a₂ {ln (R)}² + a₂ {ln (R)}³ where T is temperature in Kelvin, R is resistance in ohms, and a 9₁, 9₂, a are constants of the calibration curve. Given the following for a thermistor R T ohm °C 1101.0 25.115 911.S 30.151 656.0 40.120 451.1 50.128 Approximate the value of temperature in °C for a measured resistance of 900 ohms. (Use any method)arrow_forward8. It is thought that the period T of a planet's year is related to r, its mean distance from the sun, by an equation of the form T = Kr" where k and n constants. If T is measured in Earth-years and r in astronomical units of distance, the values for the six inner planets are: r T Mercury 0.3871 0.2408 Venus 0.7233 0.6152 Earth 1.000 1.000 Mars 1.524 1.881 Jupiter 5.203 11.86 Saturn 9.539 29.46 Use natural logarithms to plot these values as an approximate straight line. From your graph of In T against In r find the gradient of the graph and hence the values of n and k.arrow_forwardEliminate the arbitrary constants on the given equationarrow_forward
- 4. A car supported by a MacPherson strut (shock absorber system) travels on a bumpy road at a constant velocity v. The equation modeling the motion of the car is Tut 80x + 1000x = 2500 cos where r = x (t) represents the vertical position of the cars axle relative to its equilib- rium position, and the basic units of measurement are feet and feet per second (this is actually just an example of a forced, un-damped harmonic oscillator, if that is any help). The constant numbers above are related to the characteristics of the car and the strut. Note that the coefficient of time t (inside the cosine) in the forcing term on the right hand side is a frequency, which in this case is directly proportional to the velocity v of the car. (a) Find the general solution to this nonhomogeneous ODE. Note that your answer will have a term in it which is a function of v.arrow_forwardThis question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.If a tank holds 4000 gallons of water, which drains from the bottom of the tank in 50 minutes, then Toricelli's Law gives the volume V of water remaining in the tank after t minutes as the following. Therefore, when t = 5, the rate at which the water drains is V'(5)arrow_forward4. Given the reciprocal function, y = 1/x, if the values of x increase, then the values of y . . .(a) decrease (b) increase (c) remain constant (d) increase & decreasearrow_forward
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