Scribd
Upload
8 views2 pages

Tutorial 5

This document is a tutorial from COEP Technological University focusing on applications of ordinary differential equations in electrical circuits. It includes various problems related to capacitors, resistors, and inductors, providing equations and solutions for charge, current, and time calculations. The tutorial is coordinated by Dr. Kiran Dalvi and is intended for first-year B.Tech students in the Spring Semester 2024-25.

Uploaded by

fortnitedoreamon
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
8 views2 pages

Tutorial 5

This document is a tutorial from COEP Technological University focusing on applications of ordinary differential equations in electrical circuits. It includes various problems related to capacitors, resistors, and inductors, providing equations and solutions for charge, current, and time calculations. The tutorial is coordinated by Dr. Kiran Dalvi and is intended for first-year B.Tech students in the Spring Semester 2024-25.

Uploaded by

fortnitedoreamon
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
You are on page 1/ 2

COEP Technological University Pune

(A Public University of Government of Maharashtra, Pune-411005)


(MA-23008) Differential Equations and Complex Algebra
F.Y. B.Tech. Spring Semester 2024-25 (E and TC, Electrical, Instru )
Tutorial 5
Topic : Applications of Ordinary Differential Equations 2
Co-ordinator : Dr. Kiran Dalvi
—————————————————————————————————————

1. A capacitor C = 0.2 f arads in series with a resistor R = 20 ohms


is charged from a source E0 = 24 volts. Find the voltage v(t) on the
capacitor, assuming that at t = 0 the capacitor is completely uncharged.
(Ans : 24 (1 − e−0.025t ))

dQ Q
2. Consider the RC circuit equation R + = E(t). Determine the
dt C
charge and current at time t > 0 if R = 10 ohms, C = 2 × 10−4 f arads,
and E(t) = 100 volts. Given that Q(0) = 0.
1
(Ans : Q(t) = 50 (1 − e−500t ), I(t) = 10 e−500t )

3. The charge Q on the plate of a condenser of capacity C charged through


a resistance R by a steady voltage V satisfies the differential equation

t 
dQ Q −
R + = V . If Q = 0 at t = 0, show that Q = CV  − RC 

1 e

. Find
dt C 

t
the current flowing into the plate at any time t. (Ans : i(t) = V
R e− RC )

4. A decaying e.m.f.E = 200 e−5t is connected in series with a 20 ohm


resistor and 0.01 f arad capacitor. Find the charge and current at any time
assuming Q = 0 at t = 0. Show that the charge reaches a maximum,
calculate it and find the time when it is reached.
(Ans : t = 15 , max .of Q = 0.74)

1
5. In a circuit containing inductance L, resistance R and voltage E, the
dI
current I is given by E = RI + L . Given L = 640H, R = 250 ohm
dt
and E = 500 volts. I being zero when t = 0. Find the time that elapses,
before it reaches 90% of its maximum value. (Ans : t = 64
25 ln 10)

6. Show that the current in RL circuit when a constant e.m.f. E0 is


L
applied reaches 63% of its final value in seconds. Further if L = 10
R
henries, determine the value of R so that the current will reach 99% of its
final value at t = 1 seconds ? (Ans : R = 46.06)

7. Find the current I(t) in the RC circuit with E = 100 volts,


C = 0.25 f arads, R is variable according to
R = (200 − t) ohms, 0 ≤ t ≤ 200 sec
= 0, t > 200 sec
and I(0) = 1 amp. (Ans : I = (200)−3 (200 − t)3 and 0 )

8. Find the time when the capacitor in an RC circuit with no external


e.m.f. has lost 99% of its initial charge of Q0 Coulomb.
(Ans : t = 4.605 RC)

♦♦♦♦♦♦♦♦♦

I mean the word proof not in the sense of the lawyers, who set
two half proofs equal to a whole one, but in the sense of a
mathematician, where half proof = 0, and it is demanded for
proof that every doubt becomes impossible. - Carl Friedrich
Gauss

You might also like