Ch 26: Potential and Field

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo

Knight Calc 5th Edition

Ch 26: Potential and Field

Problema 67

Capitolo 26, Problema 67

The label rubbed off one of the capacitors you are using to build a circuit. To find out its capacitance, you place it in series with a 10 μF capacitor and connect them to a 9.0 V battery. Using your voltmeter, you measure 6.0 V across the unknown capacitor. What is the unknown capacitor's capacitance?

Guida verificata passo dopo passo

Step 1: Recall the formula for capacitors in series. The total capacitance of capacitors in series is given by:

\frac{1}{C} = \frac{1}{C}

₁+1C₂, where

C

₁ and

C

₂ are the capacitances of the individual capacitors.

Step 2: Understand that the voltage across capacitors in series is divided based on their capacitances. The voltage across a capacitor is inversely proportional to its capacitance:

V

₁ =

\frac{Q}{C}

₁ and

V

₂ =

\frac{Q}{C}

₂, where

Q

is the charge on the capacitors.

Step 3: Use the given information: the total voltage across the series combination is 9.0 V, and the voltage across the unknown capacitor is 6.0 V. This means the voltage across the 10 μF capacitor is

9.0 - 6.0 = 3.0

Step 4: Apply the relationship between voltage and capacitance for capacitors in series. Since the charge

Q

is the same for both capacitors, the ratio of voltages is inversely proportional to the ratio of capacitances:

V

₁V₂ =

C

₂C₁. Substitute

V

₁ = 3.0 V,

V

₂ = 6.0 V, and

C

₁ = 10 μF.

Step 5: Solve for the unknown capacitance

C

₂ using the ratio derived in Step 4. Then, verify the total capacitance of the series combination using the formula from Step 1 to ensure consistency.

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Capacitance

Capacitance is the ability of a capacitor to store electrical charge per unit voltage. It is measured in farads (F) and is defined as the ratio of the charge (Q) stored on one plate of the capacitor to the voltage (V) across the plates, expressed as C = Q/V. Understanding capacitance is crucial for analyzing how capacitors behave in circuits.

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Percorso guidato

08:02

Capacitors & Capacitance (Intro)

Series Capacitors

When capacitors are connected in series, the total capacitance (C_total) is less than the smallest individual capacitance. The formula for total capacitance in series is given by 1/C_total = 1/C1 + 1/C2 + ... + 1/Cn. This concept is essential for determining the overall capacitance when combining capacitors in a circuit.

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09:51

Combining Capacitors in Series & Parallel

Voltage Division in Capacitors

In a series circuit, the voltage across each capacitor is divided based on their capacitance values. The voltage across a capacitor in series can be calculated using the formula V = Q/C, where Q is the charge (same for all capacitors in series) and C is the capacitance. This principle helps in understanding how the applied voltage is distributed among the capacitors.

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07:14

RMS Current and Voltage

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