Question

For the circuit shown, what is the rate of change of the current in the inductor when: L=30mH,R =20ohm,V=12 volts, and the current in the battery is 0.3 A ? Write your answer as a magnitude, in A/s. Question 10 1 pts The switch in the figure is closed at t=0 when the current l is zero. When I=19 mA, what is the potential difference across the inductor, in volts?

Answer 1

The question pertains to the rate of change of current in an RL circuit due to an applied voltage and involves calculating the inductive time constant and related properties of the circuit using principles of Physics.

Step-by-step explanation:

The question provided is related to RL circuits and the behavior of an inductor and a resistor when a voltage is applied, which are topics in Physics. Considering the values given (L = 30mH, R = 20 ohms, V = 12 volts, I = 0.3 A), we can determine the rate of change of current through the inductor using the formula for induced EMF (E = -L(di/dt)) and Ohm's law (V = IR). The potential difference across the inductor when the current is at a certain level can be found using Faraday's Law of Induction which relates the EMF to the rate of change of flux linkage (VL = L(di/dt)).

For part (a) you would calculate the inductive time constant (tau, τ), which is the time taken for the current to reach 63.2% of its final value (τ = L/R). The percentage here is not essential for the calculation of tau but gives you an idea of how current increases over time in the RL circuit. For parts (b) and (c) you would use this time constant to evaluate the rate of change of current in the different scenarios. The final percentage of the current, the time constant, self-inductance, and the rate at which current changes are all related to the properties of the RL circuit.

Answer 2

The inductive time constant of an RL circuit is crucial in determining the behavior of current and voltage over time in response to changes, such as opening or closing switches. Initial and final values of current and voltage depend on this concept and on the characteristics of the inductor and resistor.

Step-by-step explanation:

The question relates to the behavior of an RL (resistor-inductor) circuit when it is powered by a voltage source, and specifically, it addresses the rate of change of current through an inductor. The key concept at play here is the inductive time constant (τ), which is defined as the time it takes for the current to change significantly (specifically, to about 63.2% of its final value) after a change in the circuit, such as opening or closing a switch. The time constant depends on the resistance and inductance in the circuit and is given by τ = L/R, where L is the inductance and R is the resistance. The initial current in an RL circuit is zero because the inductor opposes changes in current by generating an electromotive force (EMF), known as Lenz's law. As for the voltage across the inductor, once the current reaches a steady state, the inductor behaves like a short circuit, making the voltage across it zero, while the voltage across the resistor equals the source voltage.