Question #11.(6 pts.) Aresistor with resistance 470 is in a series with a capaci
ID: 1875934 • Letter: Q
Question
Question #11.(6 pts.) Aresistor with resistance 470 is in a series with a capacitor ofcapacitance 8.5 x 10° F. We want to determine what capacitance must be placed in parallel with the original capacitance to change the capacitive time constant of the combination to three times its original value. Write an equation for the equivalent capacitance, Ceg, of the parallel combination of the given capacitor, C, and the unknown capacitor, Cu 1 point/ write an equation for the original capacitive time constant, , in terms of the resistance and the given capacitance, C 1 point Write an equation for the capacitive time constant, t, in terms of the resistance and the equivalent capacitance of the parallel capacitors, Ceq 1 point We have these THREE equations. We are told that we want to consider the case for which the time constant, t, is three times it's original value, (t = 3 .) This is a FOURTH equation. what are the FOUR unknowns? To (given)(given)0.5 points0.5 points Four equations with four unknowns may seem "hard" or "scary" Of course you should see, however, that this is an easy problem. Most of the equations (like 3 t.) are so easy that normally we wouldn't even count it as an equation (and we wouldn't count to as an unknown). We just plug in the values as we go along with our "real" equations, making substitutions för some unknowns in lerms of others for which we have "casy" eqaations (A confident, capable, person could actuaily just wnte down a single equation, (the one given t 3 o) and just plug in the values corresponding to the three equations asked for above from their head while writing it all down, keeping only the single unknown Cu and solving the one equation with the one unknown.) Solve the equations for the unknown capacitance, Cu, which must be placed in parallel with the original capacitance to change the capacitive time constant of the combination to three times its original value 2 pointsExplanation / Answer
a) Parallel combination of capacitors : Ceq = C + Cu
b) T0 = RC
c) T = R*Ceq
d) Fourth equation is T = 3T0
the other two unknowns are ( to be filled in blanks) are Ceq , Cu
from last three equations Ceq = 3C
combining with first, Cu = 2C
= 2*8.5*10^-6
Cu = 1.7*10^-5 F answer