In an alternating current circuit consisting of elements in series, the current increases on increasing the frequency of supply. Which of the following elements are likely to constitute the circuit?

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.