Question

The first four questions give all but one piece of information about a series LRC-circuit and then ask for the remaining piece. Many of the quantities do not change from question to question, so you can reuse information. To make this more apparent, I supply the following table: Xc X Question 2 (Hz) 1.000 × 10s ? 8.000 × 10-5 1.000 × 1054.000 × io-68000 x io-s 1.000 10s 4.000 ×10-68.000 x10-s 1.000 ×105 1000.00 900.00 900.00 ? 1000.00 ? 800.00 800.00 4.000 ×10-6 For example, there is a question mark in the R column of question 2, so find the resistance of a series RLC-circuit when you know its impedance, frequency, inductance, and capacitance Note that the capacitive reactance for the first three questions are the same, so I provided you with a box to calculate this value once. Similarly, the inductive reactance of questions 2 through 4 are the same, Write the value of the sought quantity on the answer sheet. Remember, you need units and the correct 5. What is the current induced in a loop of wire with an area of 493 cm2 produced by a nearby wire that 6. A loop of wire interacts with a uniform magnetic field that linearly changes from zero to 0.600T so I provided you with a box to calculate them once number of significant digits. carries a constant current of 159 mA? in 2.00 ms. The magnetic field is perpendicular to the loop. As a result, an emf of 12.00V is induced What is the area of the loop? 7. A loop of wire with an area of 713 cm2 is arranged as shown below in relation to a long straight wire that has a current of 159 mA. There is a sudden increase in the current in the long straight wire. Will the induced current in the loop be clockwise or counterclockwise? loop I = 159mA 8. A loop of wire with an area of 800.0cm2 interacts with a uniform magnetic field that linearly changes in 2.00 ms. The magnetic field is perpendicular to the loop. As a result, an emf of 12.00 V is induced. 9, A series RLC-circuit has an impedance of 968 Ω and a phase angle of 600.. what is the resistance of 10. A series RLC-circuit has a power source with a root-mean-squared emf of 120.0V, a root-mean- By what amount does the magnetic field change? the resistor in this circuit? squared current of 300.0mA, and a phase angle of 45.0 What is the average power (the rate at which 11. A series RLC-circuit has a resistance of 323 Ω and a phase angle of 300.. what is the impedance of 12. A series RLC-circuit uses 100.0 W, has a root-mean-squared current of 300.0mA and has a phase angle 13. A series RLC-circuit has a resistance of 618 Ω and an impedance of 618 Ω, what is its phase angle? electrostatic potential energy is converted to thermal energy) of this circuit? this circuit? of 30.0. What is the root-mean-squared emf provided to this circuit?

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Answer 1

Z-1000 Q R 900 f 10 Hz, C 8x10 F Capacitive reactance is, 1 Xc = 2T fc 1 2T(10 Hz) (8x10 F) -19.9 Q Expression for impedance is, Z + (x-x) 2 (1000 ) (900 ) +(X-Xc) (1000 )(900 +(x-Xc (1000 (900 )(X-199 o (1000 -(900 = (x-19.9 /1000 -(900 ) = x-19.9 0 X - (1000 Ω)- (900 Ω, +19.9 Ω X 455.78 Inductance is, L 2Tf 455.78 Q 2π(10' H2) 72.576x10 F

(2) Z-900 f10 Hz, L 4x10 H, C 8x10 F Inductive reactance is, = 2π1 2x(10 Hz) (4x10 H) -2.512 Q Capacitive reactance is, 1 Xc 1 2 fc 1 2(10 Hz) (8x10 F) 19.9 Q Expression for impedance is Z R +(X-Xc) x-x)+,- (900 R + (X-Xc) (900 R2 (2.512 Q-19.9 Q (900 -(2.512 -19.9 O -R -(900 Ω)-(2.512 Ω-19.9 Ω. -899.83 Q (3) R-800 f = 105 Hz, L 4x10 H, C 8x103 F. Expression for impedance is, Z=R +(X-Xc) Z (800 )(2.512 -19.9 Q _ 800.188 -

(4) f = 10 Hz, L 4x10 H Z-1000 , R-800 Expression for impedance is, R + (X -Xc) Z= (1000 ) (s00 ) +(2.512 Q-Xc) (1000 (800 +(2.512 Q-Xc) (1000 -(800 =(2.512 0-Xc 1000 )(s00 n) =2.512 -Xc Xc 2.512 Q-(1000 )-(800 ) -597.488 Capacitance is, 1 Xc C 1 Xc 2T fc 1 C = 2T XC 1 2π(10, Hz) 597.488 Ω - 2.66 x10- F