Derived the expression for voltage

In summary, the conversation discusses finding the constants A1 and A2 in the expression for current in a 15 millihenry inductor at t > 0. The voltage across the inductor is known to be 58 volts at t = 0(+) seconds. The individual is seeking help in finding an equation with two unknowns to solve for A1 and A2. They mention the fact that i = 4 amperes, for t < 0 is not relevant to this part of the problem. However, they realize they were overthinking the problem and acknowledge it as an occupational hazard of smart people.
  • #1
lostinhere
12
0
The current in a 15 millihenry inductor is known to be:
i = 4 amperes, for t < 0 and
i = A1 * e -2000*t + A2 * e -8000*t amperes, for t > 0

The voltage across the inductor (assuming the passive sign convention) is 58 volts at t = 0(+) seconds.

I need to find the constants a1 and a2. I have already derived the expression for voltage @ t=0: 58=-30(a1+4*a2).

Unfortunately, I am now lost. I cannot figure out an equation with 2 unknowns. Any help would be greatly appreciated.

I don't believe the fact that i = 4 amperes, for t < 0 is significant for this part of the problem.
 
Last edited:
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  • #2
never mind, I was overthinking the problem.
 
  • #3
lostinhere said:
never mind, I was overthinking the problem.
Occupational hazard of smart people. :biggrin:
 

1. What is the equation for voltage?

The equation for voltage is V = IR, where V is voltage, I is current, and R is resistance.

2. How was the expression for voltage derived?

The expression for voltage was derived from Ohm's law, which states that voltage is equal to current multiplied by resistance. This relationship was observed and studied by German physicist Georg Ohm in the 19th century.

3. What are the units of voltage?

The units of voltage are volts (V), named after Italian physicist Alessandro Volta who invented the first battery.

4. Can the expression for voltage be applied to all circuits?

Yes, the expression for voltage can be applied to all circuits, as long as they follow Ohm's law. This law applies to most circuit components, such as resistors, capacitors, and inductors.

5. How is voltage measured in a circuit?

Voltage can be measured using a voltmeter, which is a device that measures the potential difference between two points in a circuit. It is typically connected in parallel to the circuit component being measured.

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