Q. 9

# In an alternating A. Only resistor.

B. Resistor and an inductor.

C. Resistor and a capacitor.

D. Only a capacitor.

Answer :

Option (a): If only a resistor is present there, the rms current or max current doesn’t change with frequency. This is incorrect.

Option(b):

Now, the rms current is given by:

As the source doesn’t change V_{rms} doesn’t change. Note that Z is the impedance or reactance given by:

Where X_{L} is the inductive reactance, X_{C} is the capacitive reactance and R is the resistance of the resistor.

Now, in this option there is no capacitor and hence, X_{C} must be zero. Now,

Now, the inductive reactance is given by:

where f is the frequency and L is the inductance.

From the above equation we can see that, inductive reactance and frequency have a direct relation. So, on increasing the frequency, the inductive reactance increases. Thus, the impedance () increases. Hence, I_{rms} decreases. Thus, this option is incorrect.

Option(c):

Now, in this option there is no capacitor and hence, X_{L} must be zero. Now,

Now, the capacitive reactance is given by:

where f is the frequency and C is the capacitance.

From the above equation we can see that, capacitive reactance and frequency have an inverse relation. So, on increasing the frequency, the capacitive reactance decreases. Thus, the impedance () decreases. Hence, I_{rms} increases. Thus, this option is correct.

Option (d):

Now, in this option there is no capacitor and hence, X_{L} must be zero. Also, R is zero. Now,

Now, the capacitive reactance is given by:

where f is the frequency and C is the capacitance.

From the above equation we can see that, capacitive reactance and frequency have an inverse relation. So, on increasing the frequency, the capacitive reactance decreases. Thus, the impedance () decreases. Hence, I_{rms} increases. Thus, this option is correct.

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