Two resistors $R_1 = 20.0 Omega$, and $R_2 = 10.5 Omega$ are connected with a 440 mH inductor, a 12.0 V battery and a two-way switch as shown in the diagram below. At $t = 0$, the switch ab is closed. (a) Determine the time constant for this circuit. (b) Calculate the current in the two resistors and the inductor a long time after the switch is closed. $I_{R1} = ext{ A}$ $I_{R2} = ext{ A}$ $I_L = ext{ A}$ (c) What is the voltage across the two resistors and the inductor a long time after the switch is closed? $V_{R1} = ext{ A}$ $V_{R2} = ext{ A}$ $V_L = ext{ A}$ Now the switch ab is opened and ac is closed. (d) Determine the time constant for this circuit after ac is closed. (e) What is the current in the inductor at $t = 0.005 ext{ s}$ after ac is closed? (f) What is the voltage across the two resistors and the inductor at $t = 0.005 ext{ s}$ after ac is closed? $V_{R1} = ext{ A}$ $V_{R2} = ext{ A}$ $V_L = ext{ A}$
Added by Jacob R.
Close
Step 1
0 Ω resistor, the 10.5 Ω resistor, and the 440 mH inductor in series. The time constant τ for this circuit is given by: τ = L / R where L is the inductance and R is the total resistance. In this case, R = R1 + R2 = 20.0 Ω + 10.5 Ω = 30.5 Ω. So, τ = (440 mH) / Show more…
Show all steps
Your feedback will help us improve your experience
Adi S and 86 other Physics 101 Mechanics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
A resistor and inductor are connected to a 9.0 V battery by a switch as shown. The moment the switch is closed, current flows through the circuit. The resistor has a resistance of R = 220 Ω and the inductor has an inductance of L = 135 mH. (a) At time t = 0 the switch is closed and current flows through the circuit. The current increases with time and eventually reaches a steady state value of imax. Calculate the maximum current imax in units of milliamps. (b) Calculate the time constant, τ, of the circuit, in seconds. (c) Write an equation that relates the current as a function of time i(t) to the maximum current, imax. Express the equation in terms of imax and α, where α = -t/τ.
Khoobchandra A.
A $9.00-V$ battery is connected through a switch to two identical resistors and an ideal inductor, as shown in the figure. Each of the resistors has a resistance of $100 . \Omega$, and the inductor has an inductance of $3.00 \mathrm{H}$. The switch is initially open. a) Immediately after the switch is closed, what is the current in resistor $R_{1}$ and in resistor $R_{2}$ ? b) At $50.0 \mathrm{~ms}$ after the switch is closed, what is the current in resistor $R_{1}$ and in resistor $R_{2} ?$ c) At $500 . \mathrm{ms}$ after the switch is closed, what is the current in resistor $R_{1}$ and in resistor $R_{2} ?$ d) After a long time $(>10.0 \mathrm{~s})$, the switch is opened again. Immediately after the switch is opened, what is the current in resistor $R_{1}$ and in resistor $R_{2}$ ? e) At $50.0 \mathrm{~ms}$ after the switch is opened, what is the current in resistor $R_{1}$ and in resistor $R_{2} ?$ f) At $500 . \mathrm{ms}$ after the switch is opened, what is the current in resistor $R_{1}$ and in resistor $R_{2} ?$
In the circuit shown in figure, ε = 10.0 V, R₁ = 5.00 Ω, R₂ = 10.0 Ω, and L = 5.00 H. a) Switch S is closed at t = 0. Just after the switch is closed, what is the potential difference across R₁ and across the inductor L? b) At some time t after the switch S is closed, the current in the inductor is increasing at a rate of di₂/dt = 1.00 A/s. At this instant, what are the current i₁ through R₁ and the current i₂ through R₂? c) After the switch has been closed a long time, it is opened again. Just after it is opened, what is the potential difference across R₁ and across L? d) In part c, how much time elapses before the current drops to 1/2 of its initial value?
Madhur L.
Recommended Textbooks
University Physics with Modern Physics
Physics: Principles with Applications
Fundamentals of Physics
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD