Ch. 40 - Molecules and Solids

Giancoli Douglas - Physics for Scientists and Engineers 5th edition

Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Non è quello che usi tu?Cambia libro di testo

Giancoli Douglas 5th edition

Ch. 40 - Molecules and Solids

Problema 54

Capitolo 37, Problema 54

(II) An ac voltage of 120 V rms is to be rectified. Estimate very roughly the average current in the output resistor R (42 kΩ) for (a) a half-wave rectifier (Fig. 40–39), and (b) a full-wave rectifier (Fig. 40–40) without capacitor.

Guida verificata passo dopo passo

Step 1: Understand the problem. The goal is to estimate the average current through the resistor R (42 kΩ) for two cases: (a) a half-wave rectifier and (b) a full-wave rectifier. The input voltage is given as 120 V rms, and we are working without a capacitor.

Step 2: Convert the rms voltage to peak voltage. The relationship between rms voltage (V_rms) and peak voltage (V_peak) is given by:

V_{peak} = V_{rms} \times \sqrt{2}

. Substitute 120 V for V_rms to find V_peak.

Step 3: For the half-wave rectifier, the average output voltage is approximately half of the peak voltage. Use the formula:

V_{avg} = V_{peak} / 2

. Then, calculate the average current using Ohm's Law:

I_{avg} = V_{avg} / R

, where R = 42 kΩ.

Step 4: For the full-wave rectifier, the average output voltage is approximately equal to the peak voltage. Use the formula:

V_{avg} = V_{peak}

. Then, calculate the average current using Ohm's Law:

I_{avg} = V_{avg} / R

, where R = 42 kΩ.

Step 5: Compare the results for the half-wave and full-wave rectifiers. Note that the full-wave rectifier provides a higher average current because it utilizes both halves of the AC cycle, while the half-wave rectifier only uses one half.

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RMS Voltage

RMS (Root Mean Square) voltage is a statistical measure of the magnitude of a varying voltage. It represents the equivalent DC voltage that would deliver the same power to a resistor. For an AC voltage, the RMS value is calculated as the peak voltage divided by the square root of 2, which is essential for determining the effective voltage in circuits.

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RMS Current and Voltage

Rectification

Rectification is the process of converting alternating current (AC) to direct current (DC). In half-wave rectification, only one half of the AC waveform is allowed to pass, resulting in a pulsating DC output. Full-wave rectification, on the other hand, utilizes both halves of the AC waveform, providing a smoother and more efficient DC output, which is crucial for understanding the average current in the output resistor.

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 relationship is expressed as I = V/R, which is fundamental for calculating the average current in the output resistor for both half-wave and full-wave rectifiers.

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Resistance and Ohm's Law

Pratica correlata

Domanda del libro di testo

If the current gain of the transistor amplifier in Fig. 40–49 is β = i_c/i_B = 95, what value must R_c have if a 1.0-μA ac base current is to produce an ac output voltage of 0.40 V?

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Domanda del libro di testo

(III) A 120-V rms 60-Hz voltage is to be rectified with a full-wave rectifier as in Fig. 40–40, where R = 24 kΩ, and C = 35 μF. (a) Make a rough estimate of the average current. (b) What happens if C = 0.10 μF? [Hint: See Section 26–5.]

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