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Label the components in a simple LR circuit diagram.
1: Battery (\(\mathcal{E}\)), 2: Resistor (R), 3: Inductor (L), 4: Switch
What is the effect of increasing the inductance (L) in an LR circuit?
It increases the time constant (\(\tau\)), causing the current to change more slowly.
What happens when a switch is closed in an LR circuit?
The current starts to increase, and the inductor generates a back emf that opposes the change in current.
What is the effect of energy dissipation in resistors in an LR circuit?
It leads to a decrease in the inductor's stored energy over time, as the energy is converted to heat.
What happens to an LR circuit after a very long time?
The inductor acts like a short circuit, and the current reaches its maximum value, determined by the battery's emf and the resistance.
What is the effect of increasing the resistance (R) in an LR circuit?
It decreases the time constant (\(\tau\)), causing the current to reach its steady-state value more quickly and reduces the maximum current.
What happens when the current changes in an LR circuit?
The inductor induces an emf that opposes the change in current, according to Lenz's Law.
What are the differences between the transient and steady states in an LR circuit?
Transient State: Current and voltage are changing rapidly, inductor's properties are time-dependent. | Steady State: Current and voltage are stable, inductor acts like a wire with no resistance.
Compare the behavior of an inductor immediately after a switch is closed versus after a long time.
Immediately After: Inductor resists current change, current starts at zero (if initially zero). | After a Long Time: Inductor acts like a short circuit, current reaches its maximum value (\(I = \frac{\mathcal{E}}{R}\)).
What are the key differences between resistors and inductors in a circuit?
Resistors: Dissipate energy as heat, voltage is proportional to current (Ohm's Law). | Inductors: Store energy in a magnetic field, voltage is proportional to the rate of change of current.
Differentiate between the behavior of an inductor during charging versus discharging.
Charging: Current increases exponentially from zero towards a maximum value. | Discharging: Current decreases exponentially from an initial value towards zero.
Compare the effect of increasing resistance versus increasing inductance on the time constant of an LR circuit.
Increasing Resistance: Decreases the time constant (\(\tau = \frac{L}{R}\)), leading to a faster response. | Increasing Inductance: Increases the time constant, leading to a slower response.