a) Frequency: 62.7 Hz
b) Resistance:
c) Average power: 38.6 W
Explanation:
a)
An alternating current can be written in the form
where
is the maximum current in the bulb
(1) is the angular frequency, where f is the frequency
t is the time
Here the current in the bulb is
This means that
And therefore by using formula (1), we can find the frequency:
b)
The resistance of the bulb's filament can be found by using Ohm's law:
where
V is the voltage
R is the resistance
I is the current
Here we have:
(maximum voltage)
(maximum current)
Therefore, the resistance of the bulb is
c)
In this circuit, the average power delivered to the light bulb is equal to the average power dissipated by the resistor.
For an AC circuit, the average power dissipated on a resistor is given by
where
is the rms current
The rms current can be calculated as
where in this case
is the peak current
Here the resistance is
Therefore, the average power is:
Learn more about current and resistance:
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