b SHOW un c What value does the levěl III lIMU d. The level in the right compartment has risen 6cm in 5 minutes. I'IIIU II 9 The diagram shows a simple circuit containing an inductor L and a resistor R with a dI constant applied voltage V. Circuit theory tells us that V = RI + L, where I is the current at time t seconds (we will ignore the complicated units). dt V. is a solution of the differential equation, for any a Prove that I + Ae %3D R constant A. b Given that initially the current is zero, find A in terms of V and R. c Find the limiting value of the current in the circuit. d Given that R = 12 and L = 8 x 10¯°, find how long it takes for the current limiting value. Give your answer correct to three significant figures. %3D

Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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Need help with c and d
8 A chanlU
is initially full and the II!I
The time t is measured in minutes.
dx
= k(15 – x), for some positive constant k of proportionality.
a Explain why
h. Show that x = 15 + Ae¯™ is a solution of this equation and find the value of A
c What value does the level in the left compartment approach?
d The level in the right compartment has risen 6cm in 5 minutes. Find the value of k
dt
9. The diagram shows a simple circuit containing an inductor L and a resistor R with a
constant applied voltage V. Circuit theory tells us that V = RI + L
dI
where I is
dt
the current at time t seconds (we will ignore the complicated units).
VO
+ Ae
R
is a solution of the differential equation, for any
R
a Prove that I =
constant A.
b Given that initially the current is zero, find A in terms of V and R.
c Find the limiting value of the current in the circuit.
d. Given that R = 12 and L = 8 x 10¬³, find how long it takes for the current to reach half its
limiting value. Give your answer correct to three significant figures.
proportional to the the I UI
Transcribed Image Text:8 A chanlU is initially full and the II!I The time t is measured in minutes. dx = k(15 – x), for some positive constant k of proportionality. a Explain why h. Show that x = 15 + Ae¯™ is a solution of this equation and find the value of A c What value does the level in the left compartment approach? d The level in the right compartment has risen 6cm in 5 minutes. Find the value of k dt 9. The diagram shows a simple circuit containing an inductor L and a resistor R with a constant applied voltage V. Circuit theory tells us that V = RI + L dI where I is dt the current at time t seconds (we will ignore the complicated units). VO + Ae R is a solution of the differential equation, for any R a Prove that I = constant A. b Given that initially the current is zero, find A in terms of V and R. c Find the limiting value of the current in the circuit. d. Given that R = 12 and L = 8 x 10¬³, find how long it takes for the current to reach half its limiting value. Give your answer correct to three significant figures. proportional to the the I UI
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