Chapter 31: Q40P (page 937)

An alternating source drives a series $R L C$ circuit with emf amplitude of, $6.00 V$ at a phase angle of $+ 30.0 °$ . When the potential difference across the capacitor reaches its maximum positive value of $+ 5.00 V$ , what is the potential difference across the inductor (sign included)?

Short Answer

Expert verified

The potential difference across the inductor is $- 8.00 V$ .

Step by step solution

The given data

Emf amplitude $ε_{m} = 6.00 V$
Phase angle, $ϕ = 30 °$
Potential difference across capacitor $V_{C} = 5.00 V$

Understanding the concept of phasor diagram

Using the phasor diagram and applying the Pythagorean Theorem, we can find the potential difference across the inductor. The theorem applies to the right-angled triangle relating hypotenuse, perpendicular, and base of the triangle.

Calculation of the potential difference

We have the following phasor diagram:

From the phasor diagram, we can apply the Pythagorean Theorem considering equation (i) to the diagram as follows:

$ε_{m}^{2} = V_{R}^{2} + {(V_{L} - V_{C})}^{2} V_{L} = V_{c} + \sqrt{ε_{m}^{2} - V_{R}^{2}} = V_{c} + \sqrt{ε_{m}^{2} - ε_{m}^{2} \cos^{2} ϕ} (∵ V_{R} = ε_{m} c o s ϕ, from diagram) = V_{c} + ε_{m} s i n ϕ$

For the given values, we get

$V_{L} = 5.00 V + (6.00 V) sin 30 ° = 8.00 V$

But $V_{L}$ and $V_{C}$ are $180 °$ out of the phase.

Therefore, the value of the potential difference across the inductor is $- 8.00 V$ .

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An alternating source drives a series $R L C$ circuit with emf amplitude of, $6.00 V$ at a phase angle of $+ 30.0 °$ . When the potential difference across the capacitor reaches its maximum positive value of $+ 5.00 V$ , what is the potential difference across the inductor (sign included)?

Short Answer

Step by step solution

The given data

Understanding the concept of phasor diagram

Calculation of the potential difference

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An alternating source drives a series RLCcircuit with emf amplitude of, 6.00Vat a phase angle of+30.0°. When the potential difference across the capacitor reaches its maximum positive value of+5.00V, what is the potential difference across the inductor (sign included)?

Short Answer

Step by step solution

The given data

Understanding the concept of phasor diagram

Calculation of the potential difference

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Space Physics

Mechanics and Materials

Thermodynamics

Energy Physics

Electricity

Engineering Physics

Study anywhere. Anytime. Across all devices.

An alternating source drives a series $R L C$ circuit with emf amplitude of, $6.00 V$ at a phase angle of $+ 30.0 °$ . When the potential difference across the capacitor reaches its maximum positive value of $+ 5.00 V$ , what is the potential difference across the inductor (sign included)?