PHYS121A_ Lab 218

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New Jersey Institute Of Technology *

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PHYS 121A

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Physics

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Apr 3, 2024

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pdf

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Physics Laboratory Report Lab Number and Title : Lab 223: Faraday’s Law Name : Katie Nguyen Group ID : 4 Date of Experiment : 11/30/2023 Date of Report Submission : 12/6/2023 Course and Section Number : PHYS121A - 011 Instructor’s Name : Keitarou Matsumoto Partner’s Names : Xin Jin, Caden Hendrickson, Woojeong Yoo 1. Introduction 1.1. Objectives - To understand how electromotive force (EMF) works in an inductor and look into what happens with the current in an RL circuit when it starts and stops. 1.2. Theoretical Background The equation describing the self-induced electromotive force (ε) across an inductor is ε L = -L(di/dt), where L represents the inductance of the coil, and di/dt is the rate of change of current. If the switch remains in any position long enough, establishing a constant current, and there is no change in current (di/dt = 0), the induced electromotive force across the inductor is zero. However, when there is a change in current (di/dt ≠ 0), an electromotive force (emf) exists. Kirchhoff's Voltage Law is applicable when the switch is shifted to position A, expressed as V0 - iR - L(di/dt) = 0. In this equation, V0 signifies the battery voltage, R is the loop resistance, and L denotes the coil inductance. The equation can be reformulated as i(t) = (V0/R)(1 - e^(-t/τ)), where τ is the circuit time constant (in seconds), given by L/R. Since εL = -L(di/dt), the equation VL(t) = V0e^(-t(R/L)) can be derived. Taking the natural logarithm of both sides results in ln[1 - (i(t)/i0)] = -(R/L)t, yielding a straight line. Current initiates when the switch moves from B to A, but the inductor's generated electromotive force prevents the current from reaching its maximum instantaneously. The rate of current increase is contingent on the circuit's resistance and inductance, gradually reaching its peak over time from 0. The given equation holds true when t < 0 in position A, depicting a constant current (i = V0/R): εL = -L(di/dt) = 0. At t = 0, with the switch shifted to position B, Kirchhoff’s Law of Voltages is applicable: iR + L(di/dt) = 0. This can be reexpressed as: i(t) = (V0/R)(e^(-t/τ)). Since εL = -L(di/dt) is valid, the ensuing equation can be formulated: VL(t) = V0e^(-t(R/L)). Taking the natural logarithm of both sides results in ln[i(t)/i0] = -(R/L)t, forming a linear relationship. The current ceases its flow when the switch is moved from A to B, but the inductor's generated electromotive force ensures a gradual current flow over time. The reduction in circuit current is contingent on the circuit’s resistance and inductance. 2. Experimental Procedure The instructions in the lab manual were followed with no manipulations to the experimental procedure 3. Results Data Table 1: Inductor Inductance (mH) Resistance (Ω) Current Loop 20.7 6.3 Solenoid 7.2 1.7

Solenoid: Figure showing the max voltage Figure showing the slopes of the graphs which are used to find the time constant

Current Loop: Figure showing the max voltage Figure showing the slopes of the graphs which are used to find the time constant

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