Practice Problem 23_02_2024

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Apr 3, 2024

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Practice Problem 23 02 2024 []27.2.1, Alg, 4 Consider the ( three resistors R; = 16 Q, R, = 69 R, Q, and R3 = 79 Q in the configuration shown in the figure. A potential difference AV= 2.5V is applied between A and B. R, a. Express the equivalent resistance R, of the combination of R, and R3 in terms of R, and R3. Re =Rz R3/ (Rz + R3) b. Express the total resistance R of the combination of all three resistors in terms of Ry, Ry and R3. R= R1+R2R3/(R2+R3) ¢. Calculate the numerical value of the total resistance R in Q. R=16 +69 * 79/ (69 + 79) d. Express the current I through R; in terms of the potential difference AV between A and B and the equivalent resistance R. I=AV/R e. Calculate the numerical value of I'in A. I=25/(16 +69*79 /(69 +79)) f. Express the voltage across R, AV, in terms of AV, I, and R;. AV,=AV-IR,y g. Express the current I, through R in terms of AV, and R. I;=AV, /Ry h. Calculate the numerical value of Iy in A. Ip=(25-(25*%16 /(16 +69*79/(69+79))))/ 69 i. Calculate the numerical value of I3through R3. I3=(25-(25*16 /(16 +69*79/(69+79))))/ 79 Otheexpertta.com []27.2.3, Alg, 4 A circuit made up of 6 resistors is shown in the figure, with resistances R; = 12Q, R,=65Q,R3=45Q, Ry= 62Q, Rs;=79Q, and Rg= 41 Q. The total current going through the circuitis I= 13.5A. a. Express the equivalent resistance of the combination of R4 Rs and Rg. Req = R4 + Rs + Rg b. Express the equivalent resistance of the combination of R3, R4 Rsand Rg. R'eq = (R3 R4 + R3R5 + R3 Rg) / (R3 + R4 + R5 + Rg) c. Express the equivalent resistance R of the combination of R;, R, R3, R4, R5 and R5. R= R1+R2+(R3R4+R3R5+R3R6)/(R3+R4+R5+Rs) d. Calculate the numerical value of the equivalent resistance R in Q. R=12+65+45*%(62+79+41) /(45 + 62 + 79 + 41) e. Express the potential difference between a and b, AV, in terms of the total current I and the equivalent resistance of the entire circuit R. AV=1IR f. Calculate the numerical value of AVin V. AV=(12+65+45*(62+79+41)/(45+62+79 +41)) *13.5 Otheexpertta.com [[]27.2.22, Alg, 4 In the figure, these three resistors are connected to a voltage source so that R, = 5.25Qand R3 = 9.5Qarein parallel with one another and that combination is in series with Ry = 1.5Q. a. Calculate the power being dissipated by the third resistor R3, in watts. P; =12722/(9.5*%(1.5/525+15/95+1)"2) W b. Find the total power supplied by the source, in watts. \(P_\text{total} = 1222 / (1.5 + 5.25 ¥ 9.5 / (5.25 + 9.5) ) w 120V [(]27.2.29, Alg, 3 A circuit is constructed as shown in the diagram to the right with resistance values R; = 85.5 Q, R, =545 Q,R3 =722 Q, Ry = 50.6 Q, Rs = 130.1 Q, and Rg = 103.9 Q. ¢ a. In terms of the individual -T- resistances, enter an expression for the equivalent resistance of the resistor configuration in circle A. Ry =1/ ((R3 +Rg) / (R3 Ra)) b. In terms of the individual resistances, enter an expression for the equivalent resistance of the resistor configuration in circle B. Rg =Ry +1/((R3+ Ry)/ (R3Ry)) c. In terms of the individual resistances, enter an expression for the equivalent resistance of the resistor configuration in circle C. Rc =1/ ((Rs + Rg) / (R5 Rg)) d. In terms of the individual resistances, enter an expression for the equivalent resistance of the resistor configuration in circle D. Rp =Rz +1/ ((Rs + Rg) / (Rs R¢)) e. In terms of the equivalent resistances Rg and Rp that were obtained in Part (b) and Part (d), enter an expression for the equivalent resistance of the full circuit. R =1/ ((Rg + Rp) / (Rg Rp)) f. Calculate equivalent resistance, in ohms, of the full circuit. R=1/(1/(855+1/(1/72.2+1/506))+1/(545+1 /(1/130.1+1/103.9))) Q .[{//:n-, L.

[]27.2.32, Alg, 3 A circuit is constructed, as shown, with resistance values R; = 67.9 Q, Ry =31.8Q,R3 =257 Q, Ri and Ry = 71.1 Q. ] a. In terms of the individual resistances, enter an expression for \ ’ the equivalent resistance of the resistor configuration in circle A. hall Rs Ra =1/ ((R2 +R3) / (R R3)) b. In terms of resistances R , R4, and the equivalent resistance Ra from Part (a), enter an expression for the equivalent resistance of the full circuit. R =1/ ((Ry + Rg + Rp) / (R Ry + R4 Ryp)) c. Calculate for the equivalent resistance, in ohms, of the full circuit. R=1/(1/(679+1/(1/318+1/257))+1/711) Q []27.2.36, Alg, 3 A Vo = 325 V voltage source R appears in the circuit shown along with four resistors. The resistance values are R; = 286 kQ, R, = 147 kQ, and Ry = 419 kQ. T a. What is the magnitude of the potential difference, in volts, across resistor R; ? Vi=((3@25/(419+1/(1/286+1/(2*%147))))*(1 1/286+1/(2*%147))) V Vo leftmost resistor with resistance value R; ? V, =(325/(419+1/(1/286+1/(2*%147))))*(1 1/286+1/(2%147)))/2 V ¢. What is the magnitude of the potential difference, in volts, across resistor R3 ? V3 =325-(325/(419+1/(1/286+1/(2*147))) (L/(1/286+1/(2*%147))) V AAA []27.3.2 (T), Alg, 3 Consider the circuit diagram depicted in the figure. a. What equation do you get when you apply the loop rule to the loop abcdefgha, in terms of the variables in the figure? 0=-IRy+&1-Ir; +1I3 Rz3+I3rp-8;3 b. If the current through the top branch is b, = 0.075 A, what is the current through the bottom, I, in amps? I3=(-18 + 45 + 0.075 * (2.5 + 0.5) ) / (1.5 + 0.5) E,=4av WYY, . @Review : [J27.3.3, Alg, 5 Consider the circuit diagram in the figure. a. What is the equation which results when applying the loop rule g, to loop aedcba, in terms of the 25Q variables given in the figure? 0=I;Ry +Irr;-&; +IRy b. If the current through the middle part of the loop is I} = 4.75 amps, what is the current through the top loop, I, in amps? I,=(18-6 * (18 * (0.5 + 1.5)+45* (0.5 + 2.5) ) / ((0.5+25)*(0.5+1.5)+6 ¥*(0.5+1.5+05+ 2.5)))/ (0.5 + 2.5) €,- 45V Otheexpertta.com '.t(\f\{ A - ( @Review : [[]27.3.8, Alg, 4 Consider the circuit in the diagram, with sources of emf listed below. g 1) a. Find I; in amps. W—te I; = ((25 - 46) * 118.75 + Sossa (46 + 9.5 - 49) * 40.5) / 1) (78.25 * 40.5 + 25.1 * 118.75) b. Find L, in amps. I, = (78.25 * (((25 - 46) * 118.75 + (46 + 9.5 - 49) * 40.5) / (78.25 * 40.5 + 25.1 * 118.75) ) -46 - 9.5 + 49) / ( - 118.75) c. Find I3 in amps. I3 = ((25 - 46) * 118.75 + (46 + 9.5 - 49) * 40.5) / (78.25 * 40.5 + 25.1 * 118.75) + (78.25 * (((25 - 46) * 118.75 + (46 + 9.5 - 49) * 40.5) / (78.25 * 40.5 + 25.1 * 118.75) ) -46 - 9.5 + 49) / ( - 118.75) Otheexpertta.com Yy . = (O/ Review : []27.3.9, Alg, 4 Consider the following circuit of three resistors bplec 7 d (Ry, Ry, and R3), with batteries that have emfs &1 = 25V and &, = 38.5V, and internal resistances ry and n. a. Find the current Iy, in amps. I, =(38.5* 1.5+ 25)/ (0.5 +25+6*(1+1.5)) b. Find the current I, in amps. IL,=(25-6*((38.5* 1.5+ 25)/(0.5+25+6*(1+ 1.5))))/ (0.5 + 2.5) c. Find the current I3 in amps. I;=(385%15+25)/(05+25+6*(1+15))-(25-6* ((385*1.5+25)/(0.5+25+6*(1+15))))/ (05 + 2.5) Otheexpertta.com Y ° [ ré Review @ /( b. What is the magnitude of the potential difference, in volts, across the /( )*

[[]27.3.25, Alg, 3 The circuit £y R shown has three voltage sources ' | with following EMFs: & R, E =295V Ry & =747V 4 & =1085V iy & It also has four resistors with the following resistance values: Ry =327 Q Ry =325 Q Rz =214 Q Ry =191 Q a. What is the magnitude, in amperes, of the current that passes through the resistor labeled R, ? I = abs( - ((214 + 191) * (7.47 - 2.95) - (10.85 - 7.47) * 327 ) / ((214 + 191) * 325 + (325 + 214 + 191) * 327)) A *{& Review : [[]27.3.26, Alg, 3 The circuit £ s shown has three voltage sources ' | with following EMFs: & . £ =1195V R: & =147V . & =785V 4 By It also has four resistors with the following resistance values: R, =202 Q R, =135 Q R; = 184 Q Ry =121 Q a. What is the magnitude, in amperes, of the current that passes through the resistor labeled R; ? I = abs( - ((135 + 184 + 121) * (1.47 - 11.95) + 135 * (7.85 - ;1\.47) )/ (-(135+ 184 + 121) * 202-135 * (184 + 121) ) ) Wi . = /é Review : [[]27.4.14, Alg, 5 A 480 Q resistor, an uncharged 1.7 pF capacitor, and a battery with a 6.13 V potential difference are connected in series. a. What is the initial current in mA, immediately after they are connected? I=6.13 /480 * 1000 b. What is the RC time constant in s? T=480* 1.7 * 10~ -6 ¢. What is the current, one time constant after they are connected, in milliamps? I=(6.13-0.632* 6.13) / 480 * 1000 d. What is the voltage on the capacitor after one time constant in V? AV(T) = 0.632 * 6.13 [(]27.4.15 (T), Calc, 4 The circuit shown contains a voltage a S R source withemfe =449 V, a resistor with resistance R = 125 k€, and a capacitor o with capacitance C = 642 nF. When switch S is set to position a, the three circuit elements are in series. When the switch is in position b, the battery is excluded from the circuit. The switch is initially moved to position a where it remains for a sufficiently long time that the capacitor is fully charged. a. Calculate the maximum charge, in coulombs, on the capacitor. 0 =642%4.49%10~-9 C b. The switch is moved from position a, but it is not connected to position b, so the circuit not a complete circuit. What will happen to the voltage across the capacitor? The voltage will not change. The voltage will drop exponentially with time. The voltage will drop linearly with time. The voltage will immediately drop to zero. The voltage will increase linearly with time. The voltage will increase exponentially with time. The voltage will immediately rise to &. c. The switch is now moved to position b. What is the magnitude of the instantaneous current, in amperes, through resistor at the instant the switch makes contact with terminal b? I =449*%10~-3/125 A d. With time measured from the instant that switch S is closed in position b, enter an expression for the voltage across the capacitor as a function of time. V(t) =eel-t/(CR) e. With time measured from the instant that switch S is closed in position b, calculate the time, in seconds, when the charge on the capacitor is one- half of its maximum value. tip =In(2) * (125 * 642 * 10~ -6) s f. Calculate the current through the resistor, in amperes, at time t = 45.5 ms after the switch is closed in position b. I =4.49* 10~ -3 /125 * 2,.71828~(( - 45.5 * 10~3) / (125 * 642)) A Otheexpertta.com oo oo ASA <Yy 4

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