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university:courses:engineering_discovery:lab_2 [01 Mar 2016 16:06] – created Jonathan Pearson | university:courses:engineering_discovery:lab_2 [03 Jan 2018 19:35] (current) – [Observations and Conclusions] Doug Mercer | ||
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- | ===== Summer Camp Lab 2 ===== | + | ===== Introduction to RC Circuits |
- | ===== Introduction to Electronic Components and Equipment | + | {{ analogTV> |
==== Introduction ==== | ==== Introduction ==== | ||
+ | |||
+ | Resistors, capacitors, and inductors are the basic passive building blocks of many circuits. | ||
+ | ==== Objective ==== | ||
+ | To study how RC circuits behave with switched input voltages. | ||
+ | ==== Materials and Apparatus ==== | ||
+ | * Resistor and capacitor code handouts | ||
+ | * Computer running PixelPulse software | ||
+ | * Analog Devices ADALM1000 (M1K) | ||
+ | * Solderless breadboard and jumper wires from the ADALP2000 Analog Parts Kit | ||
+ | * (1) 100 KΩ resistor from the ADALP2000 Analog Parts Kit | ||
+ | * (1) 1 KΩ resistor from the ADALP2000 Analog Parts Kit | ||
+ | * (1) 47 μF capacitor from the ADALP2000 Analog Parts Kit | ||
+ | * (1) 1 μF capacitor from the ADALP2000 Analog Parts Kit | ||
+ | ==== Procedure ==== | ||
+ | - Construct the following circuit on the solderless breadboard; note the polarity of the 47 μF capacitor{{ university: | ||
+ | - Run PixelPulse and plug in the M1K using the supplied USB cable | ||
+ | - Update M1K firmware, if necessary | ||
+ | - Set up the M1K to source voltage/ | ||
+ | - Set up Channel A source waveform for a “Constant” output of 5 V. | ||
+ | - Connect a wire from Channel A to the unconnected side of the 100 KΩ resistor while monitoring the voltage on Channel B | ||
+ | - Observe the voltage on Channel B increase slowly | ||
+ | - Change the output voltage from Channel A to 0 V and measure how long it takes the voltage on Channel B to reach 0 V (theoretically the capacitor voltage never gets to 0 V, but we can get a good estimation within the measurement limitations of the M1K) | ||
+ | - Construct the following circuit on the solderless breadboard{{ university: | ||
+ | - Set up Channel A to source a 100 Hz square wave that swings between 0 V and 5 V. | ||
+ | - Observe the shape of the waveform across the capacitor. | ||
+ | - Increase the frequency of the square wave. What happens to the voltage waveform across the capacitor? | ||
+ | ==== Theory ==== | ||
+ | A capacitor is comprised of two conductors, typically called “plates, | ||
+ | |||
+ | <m>V = Q/ | ||
+ | |||
+ | If we want to determine how the voltage and current are related, it is useful to rearrange the equation as follows. | ||
+ | |||
+ | <m>Q = CV</ | ||
+ | |||
+ | Since current is the time derivative of Q, taking the first time derivative of each side - noting that C is constant - produces an expression that relates current to the rate of change of the voltage in a capacitor. | ||
+ | |||
+ | < | ||
+ | |||
+ | This can be written explicitly for the rate of change in voltage. | ||
+ | |||
+ | < | ||
+ | |||
+ | We can use this equation to study the charging of the capacitor. | ||
+ | |||
+ | The charging rate in a RC circuit depends on the RC product, which is typically called the “time constant, | ||
+ | |||
+ | < | ||
+ | |||
+ | In one time constant the capacitor reaches approximately 63% of the applied voltage, and in five time constants it reaches approximately 99.3% of the applied voltage. | ||
+ | |||
+ | ==== Observations and Conclusions ==== | ||
+ | * Capacitors store electric charge | ||
+ | * When capacitors are charged using a voltage source in series with a resistor, the rate of change in capacitor voltage slows exponentially | ||
+ | * RC circuits are characterized by the RC product, called the time constant | ||
+ | * A capacitor in a simple RC circuit moves to 63% of the difference between its current value and a step voltage applied to the circuit in one time constant | ||
+ | * A commonly accepted time for a capacitor to fully charge is equal to five time constants | ||
+ | |||
+ | **Return to [[university: |