3. We can easily find the LR circuit time constant from a graph of the current versus time. The graph shows the current as it decays to zero. a. Determine the time constant for the LR circuit. Comment: the easiest way to do this is to note that when t= TL, the current is 1(T₁)= 10e¹= 0.37 lo b. Let L-0.3 H. Determine the resistance of the circuit. CURRENT INCREASING FROM ZERO: Assume the switch is in position (b) for a long time before it is switched to position (a) at t = 0. In position (a) Kirchoff's loop rule results in a different differential equation for the current I (t). thre E-1(t)r - L dl (t) dt = 0 al to the net numb Current (mA) r 1 % im 10 20 30 time (ms) a 00000 40 50 ww R

University Physics Volume 2
18th Edition
ISBN:9781938168161
Author:OpenStax
Publisher:OpenStax
Chapter10: Direct-current Circuits
Section: Chapter Questions
Problem 94CP: Consider the circuit below, (a) What is the initial current through resistor R2? when the switch is...
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3. We can easily find the LR circuit time constant from a graph of the
current versus time. The graph shows the current as it decays to zero.
a.
Determine the time constant for the LR circuit. Comment: the
easiest way to do this is to note that when t = TL, the current is
1(T₁)= 10e¹= 0.37 lo
b. Let L-0.3 H. Determine the resistance of the circuit.
CURRENT INCREASING FROM ZERO: Assume the switch is in position (b) for a
long time before it is switched to position (a) at t = 0. In position (a) Kirchoff's
loop rule results in a different differential equation for the current I(t).
dl (t)
E-1(t)r-L- = 0
dt
The solution to this differential equation is
I(t) = 1 (1 - e-t/TL),
Where I = E/r is the current at t = ∞o and the time constant T = L/r.
Current (mA)
r
E
10
a
20 30
time (ms)
00000
b
40
ww
50
OS
R
2.9
27
2-5
Transcribed Image Text:3. We can easily find the LR circuit time constant from a graph of the current versus time. The graph shows the current as it decays to zero. a. Determine the time constant for the LR circuit. Comment: the easiest way to do this is to note that when t = TL, the current is 1(T₁)= 10e¹= 0.37 lo b. Let L-0.3 H. Determine the resistance of the circuit. CURRENT INCREASING FROM ZERO: Assume the switch is in position (b) for a long time before it is switched to position (a) at t = 0. In position (a) Kirchoff's loop rule results in a different differential equation for the current I(t). dl (t) E-1(t)r-L- = 0 dt The solution to this differential equation is I(t) = 1 (1 - e-t/TL), Where I = E/r is the current at t = ∞o and the time constant T = L/r. Current (mA) r E 10 a 20 30 time (ms) 00000 b 40 ww 50 OS R 2.9 27 2-5
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