### Analysis of Resistor Value Impact on Capacitor Charging TimeIn STEP 2, you replaced the 5.1 kΩ resistor at R1 with a 10 kΩ resistor. The time required to charge the capacitor was monitored using the red LED at D1. You compared the charging time of the capacitor with the different resistor values in series. It was observed that D1 remained lit for a significantly longer duration with the higher value resistor. How can this be best explained?#### Options:1. **The 10 kΩ resistor is nearly twice as powerful as the 5.1 kΩ resistor, allowing the capacitor to charge nearly twice as fast.** - This statement is incorrect as the capacity to charge faster is not related to the resistor being more powerful.2. **The greater potential difference across the 10 kΩ resistor, compared to the 5.1 kΩ resistor, allowed the capacitor to reach full voltage faster.** - This statement is inaccurate because a greater resistor value actually causes a lesser current and slows down the charge rate of the capacitor.3. **The greater resistance of the 10 kΩ resistor allowed less current to flow, compared to the 5.1 kΩ resistor. This caused the capacitor to charge more slowly.** - This is the correct statement. A higher resistance means less current flows in the circuit, resulting in a slower charging rate for the capacitor. Therefore, the LED at D1 will stay lit longer because the capacitor takes more time to reach its full charge.4. **My LED did not light because it was never discharged, despite the instructions to do so.** - This is a procedural error and not related to the explanation about the differences in resistor values.##### Explanation:When you use a higher resistor value (10 kΩ) in place of a lower resistor value (5.1 kΩ), it restricts the flow of current more significantly. Ohm's Law (V = IR) dictates that a higher resistance results in a lower current for a given voltage. In an RC (Resistor-Capacitor) charging circuit, the time constant (τ) is given by the product of resistance (R) and capacitance (C): τ = R*C. A larger resistance increases the time constant, making the capacitor charge more slowly. Therefore, the LED at D1 stays lit longer because it takes more time for the capacitor to accumulate charge up to the threshold level ### Educational Resource: Simple LED Circuit Diagram#### Circuit Description:This image represents a simple LED circuit diagram with the following components:1. **Power Supply**: - **PSB**: The circuit is powered by a battery or power supply providing a constant voltage of 3.3 volts (3.3 V).2. **Switch**: - **SW1**: This is a single-pole single-throw (SPST) switch used to control the circuit. When the switch is closed, the circuit is complete, and current can flow through it.3. **LED**: - **D1**: A red Light Emitting Diode (LED) indicated by its symbol and labeled as "Red". LEDs are polarized components with an anode (+) and cathode (-). The cathode is typically connected to a lower potential.4. **Capacitor**: - **C1**: A capacitor with a capacitance of 10 microfarads (10 µF). The symbol indicates that it is an electrolytic capacitor, which is polarized.5. **Resistor**: - **R1**: A resistor with a resistance value of 5.1 kilo-ohms (5.1 kΩ). The purpose of this resistor is to limit the current flowing through the LED to prevent it from being damaged by excessive current.#### Operational Explanation:- When **SW1** is in the open position, the circuit is incomplete, and no current flows through the LED, so the LED remains off.- When **SW1** is closed, the circuit is complete, resulting in current flowing from the power supply (PSB), through the LED (D1), the resistor (R1), and back to the power supply.- **D1** (Red LED) will emit light when the switch is closed, and current flows through it.- The resistor **R1** ensures that the current is within safe limits for the LED.- The capacitor **C1** might be used for filtering or stabilizing the supply voltage, though it's not typical for a simple LED circuit.This circuit is a basic example of how LEDs can be integrated into electronic circuits, demonstrating the use of fundamental electronic components like resistors, capacitors, and switches. This setup can be used for educational purposes to illustrate concepts of current flow, circuit completion, and basic electronics principles.

How longer led can lit it depends on the charging time of capacitor Charging time of capacitor…

served using the red LED at D1. You compared the charging time of the capacitor with the different resistor values series. You should have seen that D1 was lit for a significantly longer time with the higher value resistor. How is this st explained? fast. The 10KQ resistor is nearly twice as powerful as the 5k1Q resistor, allowing the capacitor to charge nearly twice The greater potential difference across the 10kQ resistor, compared to the 5k1Q resistor, allowed the capacitor to reach full voltage faster. The greater resistance of the 10kQ resistor allowed less current to flow, compared to the 5k1Q resistor. This caused the capacitor to charge more slowly. My LED did not light because it was never discharged, despite the instructions to do so.

served using the red LED at D1. You compared the charging time of the capacitor with the different resistor values series. You should have seen that D1 was lit for a significantly longer time with the higher value resistor. How is this st explained? fast. The 10KQ resistor is nearly twice as powerful as the 5k1Q resistor, allowing the capacitor to charge nearly twice The greater potential difference across the 10kQ resistor, compared to the 5k1Q resistor, allowed the capacitor to reach full voltage faster. The greater resistance of the 10kQ resistor allowed less current to flow, compared to the 5k1Q resistor. This caused the capacitor to charge more slowly. My LED did not light because it was never discharged, despite the instructions to do so.

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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