Inductors: LR & LC Circuits

What this investigation asks

An inductor opposes changes in current, which is different from acting as a permanent block to current. This investigation follows a coil's transient response and compares electrical and magnetic energy storage. Identify the total series resistance, including the real coil's resistance, before predicting the final current. The ideal inductive contribution can vanish at steady current while a resistive voltage remains across the physical coil. The goal is to connect those different contributions to the measured current-time and voltage-time records rather than assigning every coil voltage to induction.

Design and measure the comparison

Compare resistance, core position, or supply voltage in separate LR trials. Retain the starting state and time of the switching action. Estimate a time constant from the appropriate fractional response or fit instead of treating the first apparently flat portion as exact completion. Increasing resistance changes both the final current and the transient time under fixed supply voltage. A changed core alters inductance under the course model. Keep those effects separate when interpreting a faster response, since a shorter time constant does not by itself imply a larger final current.

Connect the record to the model

Use the loop account to relate source voltage to resistance and the inductive term proportional to current's rate of change. During turn-on, the induced effect opposes the growth; during a later decrease, it opposes that decrease. Magnetic energy depends on inductance and squared current. The LC comparison transfers energy between electric and magnetic storage, so current and capacitor voltage need not reach extrema at the same instant. A circuit with resistance also dissipates energy, changing the oscillation account from the loss-free reference rather than breaking energy conservation.

Interpret the evidence and its limits

Interpret measurements through sampling resolution and the finite transient duration. A real coil includes resistance, and its long-time terminal voltage can therefore remain nonzero even when the ideal inductive voltage is negligible. Compare the physical terminal reading with the separate modeled components. Retain whether a stated inductance belongs to the selected geometry and core rather than calculating it as if it were a quantity caused by the instantaneous current in the linear model. A final explanation should connect the observed approach or oscillation to the circuit constraints and the relevant energy stores.

Reference conditions and quantities

For the specified air-core LR case with external resistance 10 Ω and supply 3.0 V, total resistance is 15.70000000 Ω and reference time constant is 0.5222929936 ms. The final current is 0.1910828025 A. These values include the course coil resistance; using only the external resistor would change both the inferred transient and final-current calculation.

Use the record to test your explanation

Write a prediction before collecting the comparison, naming the quantity that should change and the condition you will alter. Keep a reference run and vary one factor at a time when the question calls for a controlled test. Record the selected apparatus settings, units, and measurement interval. Where an activity supplies Ideal and Real modes or seeded variation, retain that identity with each record rather than mixing incompatible runs in one calculation.

Separate an instrument reading or counted observation from the model relationship used to explain it. Keep raw values alongside derived results so another student can reconstruct the argument. A graph needs labeled axes and a stated comparison range. If a result differs from a reference, inspect the conditions, rounding, and measurement procedure before changing the explanation.

For a classroom discussion, compare claims supported by the same evidence and identify an additional measurement that would distinguish competing accounts. Finish with a claim, the relevant observations, and reasoning tied to this course's model. State a specific limitation instead of assigning a general error label to every disagreement.

Related investigations

Compare electric storage and exponential response in Capacitors & RC Circuits, then examine changing flux in Electromagnetic Induction. Keep terminal voltage, induced electromotive force, and resistance contributions distinct in the circuit account.