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Q: (a) What is the emf across the inductor immediately after the switch is opened? V (b) When does…
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An inductor with inductance L = 0.200 H and negligible resistance is connected to a battery, a switch S, and two resistors, R1 = 8.00 Ω and R2 = 6.00 Ω. The battery has emf 48.0 V and negligible internal resistance. S is closed at t = 0
. (a) What are the currents i1, i2, and i3 just after S is closed?
(b) What are i1, i2, and i3 after S has been closed a long time?
(c) Apply Kirchhoff’s rules to the circuit and obtain a differential equation for i31t2. Integrate this equation to obtain an equation for i3 as a function of the time t that has elapsed since S was closed.
(d) Use the equation that you derived in part (c) to calculate the value of t for which i3 has half of the final value that you calculated in part (b).
(e) When i3 has half of its final value, what are i1 and i2?
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- Initially, an inductor with no resistance carries a constant current. Then the current is brought to a new constant value twice as large. After this change, when the current is constant at its higher value, what has happened to the emf in the inductor?The battery terminal voltage in the figure below is = 7.70 V and the current I reaches half its maximum value of 7.00 A at t = 0.130 s after the switch is closed. A circuit contains a battery, a switch, an inductor, and a resistor. The circuit starts at the positive terminal of the battery labeled emf ℰ, goes through the switch labeled S, goes through the inductor labeled L, goes through the resistor labeled R and ends at the negative terminal of the battery. (a) Calculate the time constant ? (in s). ? s (b) What is the potential difference (in V) across the inductor at t = 0.130 s? ?V (c) What is the potential difference (in V) across the inductor in the instant after the switch is closed at t = 0? ?VA 3.5 mH inductor and a 4.5 mH inductor are connected in series and a time varying current is established in them. When the total emf of the combination is 16 V, what is the emf of the larger inductor?
- An electric current contains a battery that produces a voltage of 60 voltsV , a resistor with a resistance of 13 ohms, and inductor with an inductance of 5 henrys H . Using calculus, it can be shown that I I t (in amperes, A), when t seconds after the switch is closed is 13 5 60 1 13 t I e 1.4.1 Use this equation to express the time t as function of the currentI Two solenoids A and B, spaced close to each other and sharing the same cylindrical axis, have 340 and 580 turns, respectively. A current of 3.40 A in solenoid A produces an average flux of 300 uWb through solenoid A and a flux of 90.0 µWb through solenoid B. (a) Calculate the mutual inductance of the two solenoids. mH (b) What is the inductance of A? mH (c) What is the magnitude of the emf that is induced in B when the current in A changes at the rate of 0.500 A/s? mVConsider the RL direct current circuit shown. The circuit contains R = 4.0 Ω, L = 10 mH, & ε = 12 V. The circuit is charging. (a) Determine the time constant for the circuit? (b) What is the maximum current in the circuit? (c) What is the current one time constant (t = τ )? (d) When the current is 0.5 A, what is the strength of the magnetic field in the solenoid, with n = N/ℓ = 319x103 turns/m. ( T×m/A)
- Where a 44 V battery is connected to three resistors and an inductor with values R1 = 96 Ω, R2 = 24 Ω, R3 = 40 Ω, and L = 16 H. The switch has been OPEN for a LONG TIME. IMMEDIATELY AFTER we CLOSE the switch, what is the current in R3? 0.743 A 0.324 A 0.000 A 1.100 ATwo solenoids, A and B, are wound using equal lengths of the same kind of wire. The length of the axis of each solenoid is large compared with its diameter. The axial length of A is thrice as large as that of B, and A has twice as many turns as B. What is the ratio of the inductance of solenoid A to that of solenoid B?A 25-turn ideal solenoid has an inductance of (4.19x10^-3) H. To generate an EMF of (1.5x10^0) V what should be the rate of change of the current? Express your result as the magnitude in A/s.
- An inductor (L = 0.39 H) and two resistors (R, = R, = 5.5 N) are connected to a battery with an emf of 12.0 V as shown in the figure below. 12.0 V R1 S R2 (a) If the switch S is closed at time t = 0, determine the potential drop across the inductor at time t = 0.045 s. (Enter the magnitude.) V (b) After a steady state is reached, the switch is opened. What are the direction and magnitude of the current through R, at a time 0.045 s after the switch is opened?A 35.0 V battery with negligible internal resistance, a 50.0 Ohm resistor, and a 1.25 mH inductor with negligible resistance are all connected in series with an open switch. The switch is suddenly closed. How long after closing the switch will the current through the inductor reach one-half of its maximum value? How long after closing the switch will the energy stored in the inductior reach one-half of its maximum value?Consider a 22.5 mH inductor that has a resistance of 4.1 Ω. Part (a) What is the time constant, τ, of the inductor, in seconds? Part (b) If the inductor is connected to a 12.0 V battery, what is the current, I, in amperes, after 10.5 ms?