14. An inductive coil and a non-inductive resistance R ohms are connected in series across an a.c. supply. Derive expressions for the power taken by the coil and its power factor in terms of the voltage across the coil, the resistance and the supply respectively. If R= 12 Nand the three voltages are in order, 110 V, 180 V and 240 V, calculate the power and the power factor of the coil. |546 W; 0.331|
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- Please answer the following points in detail and rigorously. Instead ofresort to formulas, develop from basic principles (laws ofvoltages and currents, definition of electrical power, properties ofphasors, among others) a) Suppose that between the two terminals of an element there is a voltage v (t) and that through the terminal marked with a positive sign a current i (t). Show that if v (t) and i (t) are sinusoidal and are out of phase an angle θ, then the active power P which is consumed by this element is proportional to cosθ. b) How much is P for a pure inductor and how much for a capacitor pure? Does this make physical sense? c) When the power factor seen between two terminals is specified, Why is it necessary to indicate whether it is late or early? d) Show that the complex power consumed by two elements in parallel is the sum of the individual complex powers. After, repeat the procedure but for two elements in series. e) What meaning would you give to the P consumed by an…A coil of inductance 1 henry and a resistance of 20 ohms is connected to an emf E=200sin(20t) . What is the DE model relating the current I and time t described in the problem?Answer the following points in detail and rigorously. Instead of resorting to formulas, develop from basic principles (laws of voltages and currents, definition of electrical power, properties of phasors, among others). d) Show that the complex power consumed by two elements in parallel is the sum of the individual complex powers. Then repeat the procedure but for two elements in series. e) What meaning would you give to the P consumed by an element? Which to Q?
- A battery of emf 30.0 V is connected to a switch, an inductor of inductance ? = 0.600 ? and two resistors, R1 = 10.0 ? and R2 = 6.00?. The switch is initially open. A. What are the values of currents ?1, ?2, ?3 just after the switch is closed? (Just give an answer) ?1 = ?2 = ?3 = B.)Which point, a or b, is at higher potential or are they at the same potential, just after switch S is closed? (Just give an answer) C. What is the value of current ?1 through the battery a long time after the switch is closed? Show your work and briefly explain your logicAnswer the following points in detail and rigorously. Instead of resorting to formulas, develop from basic principles (laws of voltages and currents, definition of electrical power, properties of phasors, among others). a) Show that the complex power consumed by two elements in parallel is the sum of the individual complex powers. Then repeat the procedure but for two elements in series. b What meaning would you give to the P consumed by an element? Which to Q? c) Suppose you know P and Q for a two-terminal element. What is the power factor of this element? When would you be ahead and when would you be behind? d) Suppose you know the equivalent resistance R and the equivalent reactance X of a two-terminal passive network. What is the power factor of this network? When would you be ahead and when would you be behind?When this resultant voltage is applied to a circuit consisting of a 10-Ω resistor and a capacitance of 17.3 Ω reactance connected in series, find an expression for the instantaneous value of the current flowing, expressed in the same form
- Answer the following points in detail and rigorously. Instead of resorting to formulas, develop from basic principles (laws of voltages and currents, definition of electrical power, properties of phasors, among others). a) Suppose that between the two terminals of an element there is a voltage v (t) and that a current i (t) enters through the terminal marked with a positive sign. Show that if v (t) and i (t) are sinusoidal and are out of phase by an angle ϕ, then the active power P that is consumed by said element is proportional to cos ϕ. b) How much is P for a pure inductor and how much for a pure capacitor? Does this make physical sense? c) When specifying the power factor seen between two terminals, why is it necessary to indicate whether it is lagging or leading? d) Show that the complex power consumed by two elements in parallel is the sum of the individual complex powers. Then repeat the procedure but for two elements in series. e) What meaning would you give to the P consumed…Answer the following points in detail and rigorously. Instead of resorting to formulas, develop from basic principles (laws of voltages and currents, definition of electrical power, properties of phasors, among others). a) Suppose that between the two terminals of an element there is a voltage v (t) and that a current i (t) enters through the terminal marked with a positive sign. Show that if v (t) and i (t) are sinusoidal and are out of phase by an angle ϕ, then the active power P that is consumed by said element is proportional to cos ϕ b) How much is P for a pure inductor and how much for a pure capacitor? Does this make physical sense? c) When specifying the power factor seen between two terminals, why is it necessary to indicate whether it is lagging or leading?Please answer the following points in detail and rigorously. Instead ofresort to formulas, develop from basic principles (laws ofvoltages and currents, definition of electrical power, properties ofphasors, among others) d) Show that the complex power consumed by two elements in parallel is the sum of the individual complex powers. After, repeat the procedure but for two elements in series. e) What meaning would you give to the P consumed by an element? Which to Q? f) Suppose you know P and Q for a two-terminal element. What is the power factor of this element? When would i be in early and when behind? g) Suppose you know the equivalent resistance R and the reactance X equivalent of a two-terminal passive network. What is the factor power of red bliss? When would I be in advance and when in backwardness?
- A coil is made up of 1000 turns of 0.5 mm^2 cross-sectional area copper wire. The average length each turn is 100 cm, and the copper resistivity is 0.02 µΩ m at 20 degrees Celsius. Determine the coil's resistance. Find the resistance of the coil at 20 degrees Celsius. * 30 ohm 40 ohm 50 ohm 60 ohm Find the resistance of the coil at 100 degrees Celsius if the temperature coefficient of resistance at 30 degrees Celsius is 3.7807 x 10^(-3) per degrees Celsius * 32.57 ohm 42.57 ohm 52.57ohm 62.57 ohmAnswer the following point in detail and rigorously. Instead of resorting to formulas, develop from basic principles (laws of voltages and currents, definition of electrical power, among others). a) What meaning would you give to the P consumed by an element? Which to Q?A choke coil of resistance 8 ohm and inductance 0.15 H is connected in series with a capacitor of capacitance 125 ?? across a 230-V, 50- Hz supply. Calculate: (a) the inductive reactance, (b) capacitive reactance, (c) impedance, (d) current, (e) voltage across the coil and the capacitor, respectively. (f) phase difference between the current and the supply voltage.