Buttons

1) Reminders: Buttons

In lab this week, one of the new components we worked with was a button (a.k.a. a momentary switch if you're feeling fancy). In a circuit schematic, we'll often draw a momentary switch like so:

While the button is pressed down, its terminals are shorted together; but when we let go of the button, its terminals are again disconnected. In a second, we're going to build the following circuit:

The red "+" and "-" tags there represent the place where we'll measure our output (which will change based on whether the button is pressed or not).

When the switch is open, what is the voltage across the button (between the two labeled locations), in Volts?

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When the switch is closed, what is the voltage across the button (between the two labeled locations), in Volts?

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2) Resistance Effect

In the circuit above, we saw that the voltage changes between 0V and 10V as you push the button. But interestingly, those voltages don't depend on the particular value we chose for the resistor in the circuit.

Despite this, the particular value of resistance that we choose here can make a big difference in terms of the behavior we see from the circuit in real life. Importantly, even though the resistance value doesn't affect the voltage that we see across the button, it does affect the current flowing through the circuit (and, thus, the power dissipated by that resistor).

What is the power dissipated by the resistor when the button is pressed, when using a 1{\rm k}\Omega resistor? Enter your answer as a single number with units of Watts (Volts \times Amps):
 
p =~

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Now, let's imagine using a 10\Omega resistor instead.

What is the power dissipated by the resistor when the button is pressed, when using a 10\Omega resistor? Enter your answer as a single number with units of Watts (Volts \times Amps):
 
p =~

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Importantly, the resistors we're using in lab are designed to dissipate 1/4 Watt or less, so while using a 1{\rm k}\Omega resistor is safe, usign a 10\Omega resistor puts them well above that rating. What happens when we push the button if we're using a 10\Omega resistor? Well, this happens:

The resistor gets hot enough that it burns, drawing a lot of current until the circuit breaks, turning the resistor into an open.

3) Design

Even in cases where things don't get hot enough to burn, any power dissipated by our resistors is, in some sense, wasted; that energy is converted to heat instead of being used productively by other parts of our circuit. As such, power is often one factor that we take into account when designing circuits.

In this section, we'll design a new circuit, subject to constraints on power. Our last circuit changed the output voltage from 10V to 0V when the button was pressed. Here, we'll consider a slightly different circuit:

Choose values of R_1, R_2, and R_3 such that:

• When the button is not pressed, v=6{\rm V}
• When the button is pressed, v=5{\rm V}
• The total power consumed by the resistors in either case is less than 5mW.

Enter your resistor values below as a comma-separated list of numbers representing your resistances in Ohms. For example, if you wanted R_1 = 10\Omega, R_2 = 20\Omega, and R_3=5{\rm k}\Omega, you could enter 10, 20, 5000.
 
Resistance values: 

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