c I i 0 i C 02 ms 20 V 20 V 25 V 10 k t C e E R \u03c5 \u03a9 25 mA e t 02 ms d 17 \u03c5 C V

C i i 0 i c 02 ms 20 v 20 v 25 v 10 k t c e e r υ ω

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c. I i = 0 i C = /0.2 ms 20 V 20 V 25 V 10 k t C e E = R υ Ω = 2.5 mA e t /0.2 ms d. 17. υ C = V i + ( V f V i )(1 e t/RC ) τ = RC = (2 k Ω )(10 μ F) = 8 + (4 8)(1 e t /20 ms ) = 20 ms = 8 4(1 e t /20 ms ) = 8 4 + 4 e t /20 ms = 4 + 4 e t /20 ms υ C = 4 V(1 + e t /20 ms ) 18. V i = 10 V, V f = 2 V, τ = RC = (1 k Ω )(1000 μ F) = 1 s υ C = V i + ( V f V i )(1 e t / τ ) = 10 V + (2 V 10 V)(1 e t ) = 10 8(1 e t ) = 10 8 + 8 e t υ C = 2 V+ 8 V e t 19. V i = 10 V, I i = 0 A Using the defined direction of i C i C = (10 V 2 V) 1 k Ω e t / τ τ = RC = (1 k Ω )(1000 μ F) = 1 s i C = 8 V 1 k t e Ω and i C = 8mA e t
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338 CHAPTER 24 20. τ = RC = (5 k Ω )(0.04 μ F) = 0.2 ms (throughout) υ C = E (1 e t / τ ) = 20 V(1 e t /0.2 ms ) (Starting at t = 0 for each plot) a. T = 1 1 500 Hz = f = 2 ms 2 T = 1 ms 5 τ = 1 ms = 2 T b. T = 1 1 100 Hz = f = 10 ms 2 T = 5 ms 5 τ = 1 ms = 1 5 2 T c. T = 1 1 5 Hz = f = 0.2 ms 2 T = 0.1 ms 5 τ = 1 ms = 10 2 T 21. The mathematical expression for i C is the same for each frequency! τ = RC = (5 k Ω )(0.04 μ F) = 0.2 ms and i C = /0.2 ms 20 V 5 k t e Ω = 4 mA e t /0.2 ms a. T = 1 = 2 ms, = 1 ms 500 Hz 2 T 5 τ = 5(0.2 ms) = 1 ms = 2 T b. T = 1 100 Hz = 10 ms, 2 T = 5 ms 5 τ = 1 ms = 1 5 2 T c. T = 1 5000 Hz = 0.2 ms, 2 T = 0.1 ms 5 τ = 1 ms = 10 2 T
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CHAPTER 24 339 22. τ = 0.2 ms as above T = 1 500 Hz = 2 ms 5 τ = 1 ms = 2 T 0 2 T : υ C = 20 V(1 e t /0.2 ms ) 2 T T : V i = 20 V, V f = 20 V υ C = V i + ( V f V i )(1 e t / τ ) = 20 + ( 20 20)(1 e t /0.2 ms ) = 20 40(1 e t /0.2 ms ) = 20 40 + 40 e t /0.2 ms υ C = 20 V+ 40 V e t /0.2 ms T 3 2 T : V i = 20 V, V f = +20 V υ C = V i + ( V f V i )(1 e t / τ ) = 20 + (20 ( 20))(1 e t / τ ) = 20 + 40(1 e t / τ ) = 20 + 40 40 e t / τ υ C = 20 V 40 V e t /0.2 ms 23. υ C = V i + ( V f V i )(1 e t/RC ) V i = 20 V, V f = 20 V υ C = 20 + (20 20)(1 e t/RC ) = 20 V (for 0 2 T ) For 2 T T , υ i = 0 V and υ C = 20 V e t/ τ τ = RC = 0.2 ms with 2 T = 1 ms and 5 τ = 2 T For T 3 2 T , υ i = 20 V υ C = 20 V(1 e t / τ ) For 3 2 T 2 T , υ i = 0 V υ C = 20 V e t / τ
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340 CHAPTER 24 24. τ = RC = 0.2 ms 5 τ = 1 ms = 2 T V i = 10 V, V f = +20 V 0 2 T : υ C = V i + ( V f V i )(1 e t / τ ) = 10 + (20 ( 10))(1 e t / τ ) = 10 + 30(1 e t / τ ) = 10 + 30 30 e t / τ υ C = +20 V 30 V e t /0.2 ms 2 T T : V i = 20 V, V f = 0 V υ C = 20 V e t /0.2 ms 25. Z p : X C = 1 1 2 2 (10 kHz)(3 pF) = fC π π = 5.31 M Ω Z p = (9 M 0 )(5.31 M 90 ) 9 M 5.31 M j Ω ∠ ° Ω ∠ − ° Ω − Ω = 4.573 M Ω ∠− 59.5 ° Z s : C T = 18 pF + 9 pF = 27 pF X C = 1 1 2 2 (10 kHz)(27 pF) T = fC π π = 0.589 M Ω Z s = (1M 0 )(0.589 M 90 ) 1 M 0.589 M j Ω ∠ ° Ω ∠ − ° Ω − Ω = 0.507 M Ω ∠− 59.5 ° V scope = (0.507 M 59.5 )(100 V 0 ) = (0.257 M 0.437 M ) + (2.324 M 3.939 M ) s i s p j j Ω ∠ − ° ∠ ° + Ω − Ω Ω − Ω V Z Z Z = 6 6 50.7 10 V 59.5 5.07 10 59.5 × ∠ − ° × ∠ − ° = 10 V 0 ° = 1 10 (100 V 0 ° ) = s p θ θ Z Z = 59.5 ° 26. Z p : X C = 5 1 1 (10 rad/s)(3 pF) = C ω = 3.333 M Ω Z p = (9 M 0 )(3.333 M ) 9 M 3.333 M j Ω ∠ ° Ω Ω − Ω = 3.126 M Ω ∠− 69.68 ° Z s : X C = 5 1 1 (10 rad/s)(27 pF) = C ω = 0.370 M Ω Z s = (1M 0 )(0.370 M 90 ) 1 M 0.370 M j Ω ∠ ° Ω ∠ − ° Ω − Ω = 0.347 M Ω ∠− 69.68 ° = p s θ θ Z Z
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CHAPTER 24 341 V scope = (0.347 M 69.68 )(100 V
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