Baixe o app para aproveitar ainda mais
Prévia do material em texto
Design Problems DP 1-1 The voltage may be as large as 20(1.25) = 25 V and the current may be as large as (0.008)(1.25) = 0.01 A. The element needs to be able to absorb (25 V)(0.01 A) = 0.25 W continuously. A Grade B element is adequate, but without margin for error. Specify a Grade B device if you trust the estimates of the maximum voltage and current and a Grade A device otherwise. DP 1-2 ( ) ( ) ( )8 8 8 820 1 0.03 0.6 1 Wt t t tp t e e e e− − − −= − × = − Here is a MATLAB program to plot p(t): clear t0=0; % initial time tf=1; % final time dt=0.02; % time increment t=t0:dt:tf; % time v=20*(1-exp(-8*t)); % device voltage i=.030*exp(-8*t); % device current for k=1:length(t) p(k)=v(k)*i(k); % power end plot(t,p) xlabel('time, s'); ylabel('power, W') Here is the plot: The circuit element must be able to absorb 0.15 W. 1-9 Problems Section 1-2 Electric Circuits and Current Flow P1.2-1 ( ) ( )5 54 1 20t tdi t e edt − −= − = A P1.2-2 ( ) ( ) ( ) ( )5 5 0 0 0 0 4 40 4 1 0 4 4 4 5 5 t t t t tq t i d q e d d e d t eτ ττ τ τ τ τ− −= + = − + = − = +∫ ∫ ∫ ∫ 5− − C P1.2-3 ( ) ( ) ( ) 00 0 4 40 4sin 3 0 cos3 cos3 C3 3 t t tq t i d q d tτ τ τ τ τ= + = + = − = − +∫ ∫ 43 P1.2-4 ( ) ( ) 0t tq t i d dτ τ−∞ −∞= =∫ ∫ τ = 0 C for t ≤ 2 so q(2) = 0. ( ) ( ) ( ) 22 22 2 2t t tq t i d q dτ τ τ τ= + = =∫ ∫ = 2t−4 C for 2 ≤ t ≤ 4. In particular, q(4) = 4 C. ( ) ( ) ( ) 44 44 1 4 4t t tq t i d q dτ τ τ τ= + = − + = − +∫ ∫ = 8−t C for 4 ≤ t ≤ 8. In particular, q(8) = 0 C. ( ) ( ) ( ) 8 8 8 0 0 t t q t i d q dτ τ τ= + = +∫ ∫ = 0 C for 8 ≤ t . P1.2-5 ( ) ( ) ( )2 2 0 0 ( ) 2 0 2 2 2t t dq t i t i t t dt e t− − ⎧ <⎪= = ⎨⎪− >⎩ < < P1.2-6 5 C = 600 A = 600 s C s mgSilver deposited = 600 20min 60 1.118 = 8.05 10 mg=805 g s min C i × × × × 1-2 Section 1-3 Systems of Units P1.3-1 ( )( ) 4000 A 0.001 s 4 Cq i tΔ = Δ = = P1.3-2 9 6 3 45 10 9 10 5 10 qi t − − − Δ ×= = = ×Δ × = 9 μA P1.3-3 19 9 19 10 19 9 electron C electron C = 10 billion 1.602 10 = 10 10 1.602 10 s electron s electron electron C= 10 1.602 10 electrons C1.602 10 1.602 nA s i − − − − ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤× × ×⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ × × = × = Section 1-5 Power and Energy P1.5-1 a.) ( )( )( ) 4 = = 10A 2hrs 3600s/hr = 7.2 10 Cq i dt i t= Δ ×∫ b.) ( )( )110 V 10 A 1100 WP v i= = = c.) 0.06$Cost = 1.1kW 2hrs = 0.132 $ kWhr × × P1.5-2 ( )( ) 3 = 6V 10 mA 0.06 W 200 W s 3.33 10 s 0.06 W P wt P = Δ ⋅Δ = = = × 1-3 Section 1-3 Systems of Units P1.3-1 ( )( ) 4000 A 0.001 s 4 Cq i tΔ = Δ = = P1.3-2 9 6 3 45 10 9 10 5 10 qi t − − − Δ ×= = = ×Δ × = 9 μA P1.3-3 19 9 19 10 19 9 electron C electron C = 10 billion 1.602 10 = 10 10 1.602 10 s electron s electron electron C= 10 1.602 10 electrons C1.602 10 1.602 nA s i − − − − ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤× × ×⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ × × = × = Section 1-5 Power and Energy P1.5-1 a.) ( )( )( ) 4 = = 10A 2hrs 3600s/hr = 7.2 10 Cq i dt i t= Δ ×∫ b.) ( )( )110 V 10 A 1100 WP v i= = = c.) 0.06$Cost = 1.1kW 2hrs = 0.132 $ kWhr × × P1.5-2 ( )( ) 3 = 6V 10 mA 0.06 W 200 W s 3.33 10 s 0.06 W P wt P = Δ ⋅Δ = = = × 1-3 P1.5-3 30for 0 t 10 s: = 30 V and = 2 A 30(2 ) 60 W 15 v i t t P t≤ ≤ = ∴ = = t ( ) ( ) ( )( ) 2 25for 10 15 s: 10 30 V 80 V 5 ( ) 5 80 and ( ) 2 A 2 5 80 10 160 W t v t t b v b v t t i t t P t t t t ≤ ≤ = − + ⇒ = ⇒ = = − + = ⇒ = − + = − + ( )( ) 30for 15 t 25 s: 5 V and ( ) A 10 (25) 0 b = 75 ( ) 3 75 A 5 3 75 15 375 W v i t t i i t t P t t ≤ ≤ = = − + = ⇒ ⇒ = − + b ∴ = − + = − + ( ) ( )10 15 2520 10 15 15 25102 2 3 2 0 10 15 Energy 60 160 10 375 15 10 1530 80 375 5833.3 J3 2 P dt t dt t t dt t dt t t t t t = = + − + − = + − + − = ∫ ∫ ∫ ∫ 1-4 P1.5-4 a.) Assuming no more energy is delivered to the battery after 5 hours (battery is fully charged). ( ) ( )5 36005 3600 2 0 0 0 3 0.5 0.5 2 11 22 36003600 = 441 10 J 441 kJ t w Pdt vi d d tττ τ⎛ ⎞= = = + = +⎜ ⎟⎝ ⎠ × = ∫∫ ∫ τ b.) 1 hr 10¢Cost = 441kJ 1.23¢ 3600s kWhr × × = P1.5-5 ( ) ( ) ( ) ( ) ( )1 1 14cos3 sin 3 sin 0 sin 6 sin 6 W 12 6 6 p t v t i t t t t t⎛ ⎞= = = + =⎜ ⎟⎝ ⎠ ( ) 10.5 sin 3 0.0235 W 6 p = = ( ) 11 sin 6 0.0466 W 6 p = = − Here is a MATLAB program to plot p(t): clear t0=0; % initial time tf=2; % final time dt=0.02; % time increment t=t0:dt:tf; % time v=4*cos(3*t); % device voltage i=(1/12)*sin(3*t); % device current for k=1:length(t) p(k)=v(k)*i(k); % power end plot(t,p) xlabel('time, s'); ylabel('power, W') 1-5 P1.5-6 ( ) ( ) ( ) ( )( ) ( )8sin 3 2sin 3 8 cos 0 cos 6 8 8cos 6 Wp t v t i t t t t t= = = − = − Here is a MATLAB program to plot p(t): clear t0=0; % initial time tf=2; % final time dt=0.02; % time increment t=t0:dt:tf; % time v=8*sin(3*t); % device voltage i=2*sin(3*t); % device current for k=1:length(t) p(k)=v(k)*i(k); % power end plot(t,p) xlabel('time, s'); ylabel('power, W') 1-6 P1.5-7 ( ) ( ) ( ) ( ) ( )2 2 2 24 1 2 8 1 Wt t t tp t v t i t e e e e− − − −= = − × = − Here is a MATLAB program to plot p(t): clear t0=0; % initial time tf=2; % final time dt=0.02; % time increment t=t0:dt:tf; % time v=4*(1-exp(-2*t)); % device voltage i=2*exp(-2*t); % device current for k=1:length(t) p(k)=v(k)*i(k); % power end plot(t,p) xlabel('time, s'); ylabel('power, W') P1.5-8 =3 0.2=0.6 W 0.6 5 60=180 J P V I w P t = × = Δ = × × 1-7 Chapter 1 - Section 1 Chapter 1 - Section 2 Chapter 1 - Section 3 Chapter 1 - Section 5
Compartilhar