Jena N.

asked • 10/11/22

An electrical circuit switches instantaneously from a 8 volt battery to a 11 volt battery 7 seconds after being turned on.

An electrical circuit switches instantaneously from a 8 volt battery to a 11 volt battery 7 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.


For t < _____, V(t) = _____

For t ≥ _____, V(t) = _____


At what point or points is your function discontinuous?

t = _____

(Give your answer as a comma-separated list, or enter the word none if there are no discontinuities.)

John P.

Note: variable t - defines secs Per the question stating instantaneous switching at (t < 0) the voltage V(t) = 0 volts given the switch was turned on at t = 0. At (t < 7) the voltage V(t) = 8 volts. At t>= 7 the voltage V(t) = 11 volts. The point or points that the function is discontinuous occur at t=0, and t=7.
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10/19/22

1 Expert Answer

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Jonathan T. answered • 10/26/23

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5.0 (362)

Calculus, Linear Algebra, and Differential Equations for College

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To sketch the graph of the battery voltage against time, you have two distinct periods in this scenario:


1. For t < 7 seconds, the circuit is powered by an 8-volt battery.

2. For t ≥ 7 seconds, the circuit switches to an 11-volt battery.


So, your graph can be represented as follows:


For t < 7, V(t) = 8

For t ≥ 7, V(t) = 11


The function is discontinuous at t = 7 seconds, which is the point where the battery voltage abruptly changes from 8 volts to 11 volts.

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