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Ch 32: AC Circuits
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
All textbooksKnight Calc 5th EditionCh 32: AC CircuitsProblem 68a
Chapter 32, Problem 68a

FIGURE CP32.68 shows voltage and current graphs for a series RLC circuit. What is the resistance R?

Verified step by step guidance
1
Step 1: Observe the voltage and current graphs provided in the figure. The voltage graph (purple) and current graph (green) are sinusoidal and appear to be in phase, which indicates that the circuit is purely resistive.
Step 2: Recall Ohm's Law for a resistive circuit, which states that the resistance R can be calculated using the formula: R=V/I, where V is the peak voltage and I is the peak current.
Step 3: From the voltage graph, identify the peak voltage. The graph shows that the maximum voltage is 10 V.
Step 4: From the current graph, identify the peak current. The graph shows that the maximum current is 2 A.
Step 5: Substitute the peak voltage and peak current values into the formula for resistance: R=10/2. Simplify the expression to find the resistance.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

RLC Circuit

An RLC circuit is an electrical circuit consisting of a resistor (R), inductor (L), and capacitor (C) connected in series or parallel. The behavior of the circuit is characterized by its impedance, which combines the effects of resistance, inductance, and capacitance. Understanding the RLC circuit is crucial for analyzing how voltage and current interact over time, especially in alternating current (AC) systems.
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Phase Difference

In AC circuits, voltage and current can oscillate out of phase, meaning they reach their maximum and minimum values at different times. The phase difference is measured in degrees or radians and affects the power factor of the circuit. In the context of the given graphs, analyzing the phase difference between the voltage and current waveforms is essential for determining the resistance and overall behavior of the RLC circuit.
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Phase Constant of a Wave Function

Ohm's Law

Ohm's Law states that the current (I) flowing through a conductor between two points is directly proportional to the voltage (V) across the two points and inversely proportional to the resistance (R) of the conductor. This fundamental principle is expressed as V = IR. In the context of the RLC circuit, applying Ohm's Law helps in calculating the resistance by analyzing the relationship between the voltage and current waveforms shown in the graphs.
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Related Practice
Textbook Question

A series RLC circuit with ε0 = 10.0 V consists of a 1.0 Ω resistor, a 1.0 μH inductor, and a 1.0 μF capacitor. What is V1 at ω = ω0 and at ω = ω1?

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Textbook Question

Prove that the energy dissipation is a maximum at ω = ω₀.

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Textbook Question

A motor attached to a 120 V/60 Hz power line draws an 8.0 A current. Its average energy dissipation is 800 W. What is the motor's resistance?

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Textbook Question

A motor attached to a 120 V/60 Hz power line draws an 8.0 A current. Its average energy dissipation is 800 W. What is the rms resistor voltage?

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Textbook Question

A motor attached to a 120 V/60 Hz power line draws an 8.0 A current. Its average energy dissipation is 800 W. How much series capacitance needs to be added to increase the power factor to 1.0?

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Textbook Question

Show that the peak inductor voltage in a series RLC circuit is maximum at frequency ωL=(1ω02−12R2C2)−1/2\(\omega\)_L = \(\left\)( \(\frac{1}{\omega_0^2}\) - \(\frac{1}{2}\) R^2 C^2 \(\right\))^{-1/2}.

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