In Figure 14.12, ε = 12 V , L = 20 mH, and R = 5.0 Ω . Determine (a) the time constant of the circuit, (b) the initial current through the resistor, (C) the final current through the resistor, (d) the current through the resistor when t = 2 τ L , and (e) the voltages across the inductor and the resistor when t = 2 τ L .
In Figure 14.12, ε = 12 V , L = 20 mH, and R = 5.0 Ω . Determine (a) the time constant of the circuit, (b) the initial current through the resistor, (C) the final current through the resistor, (d) the current through the resistor when t = 2 τ L , and (e) the voltages across the inductor and the resistor when t = 2 τ L .
In Figure 14.12,
ε
=
12
V
, L = 20 mH, and
R
=
5.0
Ω
. Determine (a) the time constant of the circuit, (b) the initial current through the resistor, (C) the final current through the resistor, (d) the current through the resistor when
t
=
2
τ
L
, and (e) the voltages across the inductor and the resistor when
t
=
2
τ
L
.
A 6.0 V battery has been connected to an LR circuit for sufficient time so that a steady current flows through the resistor R=2.2kΩ and inductor L=18mH. At t=0, the battery is removed from the circuit and the current decays exponentially through R. Write the equation for the emf across the inductor as a function of time t. At what time is the emf greatest?
A circuit consists of a 0.8 H inductor and a 3.5 ohm resistor. At t = 0 the current through the inductor is 1.2 A. How much energy is stored in the inductor at this instant?
charge and the current (i) is zero, then P= 0. If q =0 at time t
=0, then =±n/2.
Example:
A 300-V dc power supply is used to charge a 25-µF capacitor. After the capacitor is fully charged, it is disconnected from
the power supply and connected across a 10-mH inductor. The resistance in the circuit is negligible. (a) Find the frequency
and period of oscillation of the circuit. (b) Find the capacitor charge and the circuit current 1.2 ms after the inductor and
capacitor are connected. Then find for the magnetic and electric energies (c) at and (d) at t = 1.2 ms.
Given:
C = 25 x 106 F
L = 10 x 103 H
t = 1.2 x 103 s
(c) Solving for magnetic (UB) and electric (UE) energies
at time t =0.
Solution:
(7.5 x 10-3 C)?
(a) Solving for angular frequency (w)and period (T)
Ug =Li? = 0
Ug =
2C
- 1.1 J
2(25 x 10-6 F)
1
= 2.03 x 10° rad/s
(10 x 10-3H)(25 x 10¬°F)
(d) Solving for magnetic (UB) and electric (UE)
energies at time t =1.2 ms.
2. 03 х 103 Рad
Ug = }Li² = }(10 × 10-3 H)(-10 A)² = 0.5 J
f
= 320…
University Physics with Modern Physics (14th Edition)
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