
An electric lamp which runs at DC and consumes current is connected to AC mains at , cycles with a choke coil in series. Calculate the inductance and drop of voltage across the choke. Neglect the resistance of the choke.
Answer
495.6k+ views
Hint: Use the relation between the voltage drop across resistor and the voltage drop across inductor. Use the relation between the reactance, frequency and current to determine the inductance of the choke.
Formula used:
The voltage drop is given by
…… (1)
Here, is the voltage drop across the resistor and is the voltage drop across the inductor.
The voltage drop across inductor is given by
…… (2)
Here, is the current and is the reactance.
The inductive reactance is given by
…… (3)
Here, is the angular frequency and is the inductance.
Complete step by step answer:
An electric lamp which runs at DC and consumes current is connected to AC mains at , cycles with a choke coil in series.
Calculate the drop of voltage across the choke.
Rearrange equation (1) for the drop across inductor.
Substitute for and for in the above equation.
Hence, the voltage drop across the choke is .
Determine the inductance of the choke.
Substitute for in equation (2).
Rearrange the above equation for the inductance .
Substitute for , for , for and for in the above equation.
Hence, the inductance is .
Hence, the inductance and drop of voltage across the choke are and respectively.
Note:
If the resistance of the choke is not neglected, one may get the results other than the obtained.
Also note that you have to remember all the formulas and how to apply the formula in the specific numericals.
Formula used:
The voltage drop
Here,
The voltage drop
Here,
The inductive reactance is given by
Here,
Complete step by step answer:
An electric lamp which runs at
Calculate the drop of voltage
Rearrange equation (1) for the drop across inductor.
Substitute
Hence, the voltage drop across the choke is
Determine the inductance of the choke.
Substitute
Rearrange the above equation for the inductance
Substitute
Hence, the inductance is
Hence, the inductance and drop of voltage across the choke are
Note:
If the resistance of the choke is not neglected, one may get the results other than the obtained.
Also note that you have to remember all the formulas and how to apply the formula in the specific numericals.
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