E17R.1 Consider the circuit shown below. Assume that the coil has a huge inducta
ID: 3163292 • Letter: E
Question
E17R.1 Consider the circuit shown below. Assume that the coil has a huge inductance (so that L/R 1 s) and that both the coil and the resistor have a resistance about 20 times smaller than that of the bulb.
Use Lenz’s law and the idea of self-inductance to answer the following questions. Be sure to explain your reasoning in detail in each case.
(a)
Predict what will happen to the bulb’s brightness when the switch is closed. (Hint: Before the switch is closed, the coil has zero current flowing through it, and the coil is initially going to want to keep it that way when the switch is closed. How can the coil arrange to have essentially zero current flowing through it? If we define the coil’s effective resistance to be the potential difference across it divided by the current flowing through it, what is the coil’s effective resistance at the instant that the switch is closed? How does this effective resistance change with time?
(b)
Predict what will happen to the bulb’s brightness when the switch is opened.
(c)
When the switch contacts are opened, one often sees bright sparks arcing across the gap between the opening contacts. Why?
Thanks for your help!
(a)
Predict what will happen to the bulb’s brightness when the switch is closed. (Hint: Before the switch is closed, the coil has zero current flowing through it, and the coil is initially going to want to keep it that way when the switch is closed. How can the coil arrange to have essentially zero current flowing through it? If we define the coil’s effective resistance to be the potential difference across it divided by the current flowing through it, what is the coil’s effective resistance at the instant that the switch is closed? How does this effective resistance change with time?
(b)
Predict what will happen to the bulb’s brightness when the switch is opened.
(c)
When the switch contacts are opened, one often sees bright sparks arcing across the gap between the opening contacts. Why?
Switch Resistor Inductor L Battery Bulb (resistance R)Explanation / Answer
(a) The effective resistance of the coil at the instant of closing the switch is V/I= infinity. It tries to maintain the inertia according to the Lenz law. That is the entire current will be through the bulb intially and it will glow intensly. But as the resistance of the coil is small compared to other resistors or bulb the current will try to flow through the coil over time. As a result the current through the bulb will decrease over time and it will be less intense gradually.
(b) When the switch is opened the coil will act like the battery or the power source for the bulb and it will try to maintain the current. Due to the heat loss the current will decrease gradually and eventually be zero. So the bulb will behave accordingly and eventually turn off.
(c) According to the Lenz law there will be a tendency to maintain the current or the connection. Henceforth the conduction electrons pile up at the end, resulting a huge electric field in that gap, causing the dielectric breakdown of the air and hence the spark.
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