What Happens to di/dt When a Switch in an Inductor Circuit Opens?

  • Thread starter hobbs125
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In summary, the problem involves a circuit with a 10v battery, 1 henry inductor, and a switch in series with a total resistance of 10k ohms. The maximum current in the inductor is 1mA and the switch is suddenly opened. The question is how to calculate di/dt in this scenario. The relevant equation is V=L x di/dt, and it is necessary to consider the switch being closed and open in order to solve the differential equation and find i as a function of time. A drawing of the circuit would be helpful to fully understand the problem.
  • #1
hobbs125
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Homework Statement



A circuit has a 10v battery, an 1 henry inductor, and a switch connected in series. The circuit's total resistance is 10k ohms. If the inductors maximum current is 1mA and the switch is suddenly opened how do I calculate di/dt?

Wouldn't the open switch be an infinite impedance and produce infinite voltage across the inductor?


Homework Equations



V=L x di/dt

The Attempt at a Solution



Not sure where to even start?
 
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  • #2
first consider the switch is closed and current is flowing at steady rate(think about it, why it should flow at a steady rate? if u don't know it already), the value is given as 1mA. u can also calculate it from given data (how?), had it not given.
now consider the switch is suddenly open. the physical consideration should be, the applied voltage is zero (and not the resistance is infinity. why?).
now set up the ckt eqn. considering potential drops across the inductor and the resistor and applied voltage zero. solve the differential eqn (u will need the value i initial = 1 mA here). and find i as a function of t. put the given values for inductor and resistor and find di/dt by differentiation.
 
  • #3
Can you provide a drawing of the circuit? The problem seems a bit strange for an intro physics class.
 

1. What is di/dt and why is it important to calculate?

DI/DT stands for change in current over change in time, and it is an important concept in electrical engineering and physics. It measures the rate of change of electric current, which is crucial in understanding how electrical circuits behave and how to design them effectively.

2. How do I calculate di/dt?

To calculate di/dt, you will need to first measure the change in current (di) and the change in time (dt). Then, divide the change in current by the change in time, using the formula di/dt = (I2 - I1) / (t2 - t1). This will give you the average rate of change of current over the given time interval.

3. What units is di/dt measured in?

Di/dt is typically measured in Amperes per second (A/s) or Amperes per microsecond (A/μs). However, the units can vary depending on the specific context and application.

4. Can di/dt be negative?

Yes, di/dt can be negative. This indicates that the current is decreasing over time. A positive di/dt indicates that the current is increasing.

5. What are some practical applications of calculating di/dt?

Calculating di/dt is useful in various fields, such as electrical engineering, physics, and electronics. It can be used to design and optimize circuits, analyze the behavior of electrical systems, and predict the performance of electronic devices. It is also important in understanding and mitigating the effects of inductance and capacitance in circuits.

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