An electrical circuit switches instantaneously from a 3 volt battery to a 22 volt battery 8 seconds after being turned on. Sketch on a sheet of paper a graph the battery voltage against time. Then fill in the formulas below for the function represented by your graph.
horizontal line at y=3 for 0<=x<=8 then horizontal line at y=22
To sketch the graph of battery voltage against time, we need to consider the two different voltage levels and the timing at which the switch occurs.
Let's assume that the voltage is initially 3 volts and then switches to 22 volts after 8 seconds. We can represent this graphically as follows:
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22 V | _________
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3 V |__________________________>
0 8 seconds
The graph has a horizontal line at 3 volts initially, representing the voltage of the circuit during the first 8 seconds. Then, there is a vertical line at 8 seconds where the voltage instantly switches to 22 volts. After that point, the graph is a horizontal line at 22 volts.
Now, let's fill in the formulas for the function represented by this graph:
For the time interval from 0 to 8 seconds, the formula for the voltage can be written as:
V(t) = 3 volts, where t is the time in seconds (0 ≤ t ≤ 8)
For the time interval after 8 seconds, the formula for the voltage can be written as:
V(t) = 22 volts, where t is the time in seconds (t > 8)
Note that these formulas represent a step function, where the voltage remains constant for each time interval.