Answered: In the circuit below, a battery…

In the circuit below, a battery supplies a constant voltage of 40 V, the inductance is 2 H, the resistance is 10 2, and I(0) = 0. switch (a) Find I(t). (b) Find the current after 0.1 s.

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter14: Inductance

Section: Chapter Questions

Problem 14.8CYU: Check Your Understanding (a) If the current in the circuit of in Figure 14.12(b) increases to 909 of...

See similar textbooks

Related questions

Q: An inductor with an inductance of 7.50 H and a resistance of 8.00 ohms is connected to the terminals…

A: a)The required rate of electrical energy just after circuit is completed is,

Q: An inductor of inductance 6.0H and resistance 640 ohms is connected in series to two resistors which…

A: Given: The value of first resistor is R1=640 Ω The inductor has a value of L=6 H. Out of the…

Q: An electromagnet can be modeled as an inductor in series with a resistor. Consider a large…

A: The inductance L=13.0 H The resistance R=3.50 Ω The emf of the battery V=18.0 V The maximum current…

Q: In the circuit shown in the figure, the inductor has inductance ?=2.75 HL=2.75 H and negligible…

Q: The switch in the figure below is open for t < 0 and is then thrown closed at time t = 0. Assume…

Q: A 30-V emf is connected in series to an inductance of 0.1 henry and a resistance of 50 Q. Initially,…

Q: A current changing at a rate of 5 A/s in a coil of inductance 5 H induces an EMF of: O a. 1 V in the…

A: The expression for emf is ε=-MdIdt

Q: A device is turned on and 3.00 A flows through it 0.100 ms later. What is the self-inductance of the…

A: Given: change in current, di = 3 A time taken, dt = 0.1 ms = 1 x 10-4 s induced emf, e = 150 V

Q: there's a man working on a circuit in this diagram. what is criterion as result of time E=5v R R1=2…

Q: A circuit consists of a large electromagnet that has an inductance of 48.0 H and a resistance of…

A: Inductance (L) = 48 H Resistance (R) = 7.9 ohm Vb = 250 V Maximum current (Im) = VbR= 2507.9= 31.645…

Q: Consider a 23 mH inductor that has a resistance of 4.15 Ω. Time constant is 0.00554. If the…

A: Given that L=23 mH R=4.15Ω Time constant τ=0.00554 s

Q: A resistor, inductor, and a battery are arranged in a circuit. The circuit has an inductance of L =…

A: Given Data: The inductance of a circuit is, L=2 H The resistance in a circuit is, R=1.8 kΩ The…

Q: If the current in an inductor is doubled, by what factor is the stored energy multiplied? (a) 4 (b)…

Q: An inductor with an inductance of 5.75 H and a resistance of 9.00 2 is connected to the terminals of…

A: Given The inductance of the inductor is L = 5.75 H. The value of resistance is R = 9 Ω. The voltage…

Q: A 12.6-V battery is in series with a resistance of 0.304 Ω and an inductor. (a) After a long time,…

Q: a circuit having an inductance of L=2mH has a current that varies with time as I=t^3e^-t. find the…

A: Emf induced can be given by, ∈=LdIdt where L is inductance and I is current and t is time. To be…

Q: A battery is connected in series with a 5Ω resistor and an inductor, as shown in the figure. The…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: A series circuit consists of a resistor with R = 20 0, an inductor with L = 1 H, a capacitor with C…

A: Here we'll find the complimentary and particular solutions of the 2nd order differential equation to…

Q: In the figure below, a 13.0 V ideal battery, a 23.302 resistor, and an inductor are connected by a…

Q: The figure below shows a circuit consisting of a 24.0 V battery in series with an inductor with…

A: It is given that, V=24 V, L=10.5 H, and R=8.00 Ω.

Q: A circuit contains a battery, a switch, an inductor, and a resistor. The circuit starts at the…

A: (a) Imax= 3.2 A (b) Time constant = 1.533 (c) t= 4.58 seconds

Q: A piece of electrical component inside a gaming laptop uses a source of electromotive force,…

A: The initial current in the circuit is I0=0.6 A The emf is 4 volt The value of the resistance is R=2…

Q: A circuit consists of a large electromagnet that has an inductance of 48.0 H and a resistance of…

Q: Show that the self-inductance per unit length of an infinite, straight, thin wire is infinite.

A: From Ampere’s law

Q: QUESTION 1 If a current of 5A flowing in a coil of inductance 0.1H is reversed in 10ms, emf induced…

A: Note: According to our guideline, I am going to solve 1st question. Please post other questions…

Q: If two coils placed next to one another have a mutual inductance of 7.50 mH, what voltage (in V) is…

Q: An RL circuits is made of a 9.5V battery, a switch, a 0.48H inductor, and a 534 resistor. What is…

Q: The closed circuit shown below (same as #1) has a resistor of 5 Ω, an inductor of 6 mH, and a…

Q: If the current in an inductor is doubled, by what factor is the stored energy multiplied?

A: If the current in an inductor is doubled, by what factor is the stored energy multiplied?

Q: Current in a circuit falls from 5.0 A to 0.0 A in 0.1 s. If an average emf of 200 V induced, give an…

A: The initial current is 5.0A, Final current is 0.0A, time taken is 0.1s, and the average emf is 200V.…

Q: If you triple the inductance of an inductor, by what factor will the amount of energy it can store…

A: The expression for the amount of energy stored in the inductor is given as U=12LI2 *Here L is the…

Q: A cr IS constructed one inductor, one battery and a switch as shown. The values for the resistors…

Q: voltage across an inductor is 4.0 x 10-6 V when the current through it decreased at a rate of 4.0…

A: Given VL = 4 × 10-6 V Rate of change of current dI/dt = -4 A/s

Q: The self-inductance of the circuit in the figure below is 9.20 10-8 H. Find the back emf when the…

Q: Aseries circuit contains a resistor with R = 40Ω, an inductor with L = 2 H, a capacitor with 0.0025…

A: Given : Resistor, R = 40 Ω Inductor, L = 2 H Capacitor, C = 0.0025 F Voltage, V(t) =…

Q: What is the self-inductance per meter of a coaxial cable whose inner radius is 0.50 mm and whose…

A: R = 4 mm r = 0.5 mm

Q: A 12 volte battery is connected to a simple series circuit in which inductor is H and the resistance…

Q: A 20.0 kHz, 16.0 V source connected to an inductor produces a 2.00 A current. What is the…

Q: A circuit consist of an inductor of inductance value P and a resistor of a resistance value 46 N.…

Q: 1, Consider the circuit shown in the figure. The battery has emf ɛ = 30 volts and negligible…

Q: An inductor with inductance 15.34H and a resistor w/ resistance 3.432 are connected in series to a…

Q: What resistance R should be connected in series with an inductance L= 220 mH and capacitance C= 12.0…

A: Assume it is a RLC circuit, thus the expression for the time of N cycles is given is,

Concept explainers

Electromagnets

The word "electromagnet" is composed of two words, ‘electro’ and ‘magnet’. It is a type of magnet in which an electric current helps in the generation of a magnetic field. Electromagnets usually consist of two major parts, wire and a coil around which the wire is wound. This is called a solenoid. When an electric current is allowed to pass through the coiled wire, the electric current produces a magnetic field. This magnetic field is present only when current is passing through the wire.

Question

In the circuit below, a battery supplies a constant voltage of 40 V, the inductance
is 2 H, the resistance is 10 N, and I(0) = 0.
%3D
E
switch
(a) Find I(t).
(b) Find the current after 0.1 s.

Expert Solution

Given data:

Supply voltage, $V = 40 V$

The inductance, $L = 2 H$
The resistance, $R = 10 Ω$

Solution for (a):

Let the current flowing through the circuit be $I$ . Apply Kirchhoff's voltage law to the circuit.

$V - i R - L \frac{d i}{d t} = 0$

Solve for current $I$ ,

$\begin{array}{rcl} V - i R & = & L \frac{d i}{d t} \\ \frac{d t}{L} & = & \frac{d i}{V - i R} \end{array}$

Integrate on both sides,

$\int_{0}^{t} \frac{d t}{L} = \int_{0}^{I} \frac{d i}{V - i R}$

Substitute $z = V - i R \Rightarrow \frac{d z}{d i} = - R$

$\begin{array}{rcl} \frac{t}{L} & = & - \frac{1}{R} \int_{} \frac{d z}{z} \\ \frac{t}{L} & = & - \frac{1}{R} \ln (z) \\ - \frac{R t}{L} & = & \ln (z) \end{array}$

Resubstitute $V - i R = z$

$\begin{array}{rcl} - \frac{R t}{L} & = & \ln {(V - i R)}_{0}^{I} \\ - \frac{R t}{L} & = & \ln (V - I R) - \ln V \\ - \frac{R t}{L} & = & \ln (\frac{V - I R}{V}) \\ e^{- \frac{R t}{L}} & = & \frac{V - I R}{V} \\ V \cdot e^{\frac{- R t}{L}} & = & V - I R \\ I R & = & V - V \cdot e^{- \frac{R t}{L}} \\ I (t) & = & \frac{V}{R} (1 - e^{- \frac{R t}{L}}) - - - (1) \end{array}$

Step by step

Solved in 3 steps

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

A steady current flows through a circuit with a large induct3ve time constant. When a switch in the circuit is opened, a large spark across the terminals of the switch. Explain.
In an oscillating LC circuit the maximum charge on the capacitor is 2.0 × 10-6 C and the maximum current through the inductor is 8.0 mA. (a) What is the period of the oscillations? (b) How much time elapses between an instant when the capacitor is uncharged and the next instant when it is fully charged?
What is the self-inductance per meter of a coaxial cable whose inner radius is 0.50 mm and whose outer radius is 4.00 mm?
Does the time required for the current in an RL circuit to reach any fraction of its steady-state value depend on the emf of the battery?
Show that the self-inductance per unit length of an infinite, straight, thin wire is infinite.
What resistance R must be connected in series with a 200-mH inductor of the resulting RLC oscillating circuit is to decay to 50% of its initial value of charge in 50 cycles? To 0.10% of its initial value in 50 cycles?
Show that N m /l and el(dl/dt), which are both expressions for se1f-inductance, have the same units.
Check Your Understanding (a) If the current in the circuit of in Figure 14.12(b) increases to 909 of its final value after 5.0 s, what is the inductive time constant? (b) If R=20 , what is the value of the self-inductance? (c) If the 20 resistor is replaced with a 100 resister, what is the time taken for the current to reach 90% of its final value?
The self-inductance and capacitance of an oscillating LC circuit are L = 20 mH and C = 1.0 F , respectively. (a) What is the frequency of the oscillation? (b) If the maximum potential difference the plates of the capacitor is 50 V, what is the maximum current in the circuit?
Check Your Understanding (a) Calculate the self-inductance of a solenoid that is tightly wound with wire of diameter 0.10 cm, has a cross-sectional area of 0.90 cm2, and is 40 cm long. (b) If the current through the solenoid decreases uniformly from 10 to 0 A in 0.10 s, what is the emf induced between the ends of the solenoid?
When a camera uses a flash, a fully charged capacitor discharges through an inductor. In what time must the 0.100-A current through a 2.00-mH inductor be switched on or off to induce a 500-V emf?
Two coils close to each other have a mutual inductance of 32 mH. If the current in one coil decays according to I=I0eat , where I0= 5.0 A and =2.0103s1 , what is the emf induced in the second coil immediately after the current starts to decay? At t=10.0103s? ?