To reduce the resonant frequency in an LCR series circuit with a generator
The resonant frequency of a RLC ac circuit is given by:
where L is the net inductance in the circuit and C is the net (equivalent) capacitance in the circuit.
The resonant frequency does NOT depend on the generator frequency. In fact, resonant frequency is a special value for the generator frequency! Hence, (a) is wrong.
Adding another capacitor in parallel will increase the net capacitance (Capacitances simply add up in parallel). From the above equation we can see that on increasing the capacitance, the resonant frequency will decrease. Hence, (b) is the correct answer.
Removing the iron core will reduce the inductance of the inductance. From the above equation we can see that on reducing the inductance, the resonant frequency will increase. Hence, (c) is an incorrect option.
Removing the dielectric will reduce the capacitance of the capacitor. From the above equation we can see that on reducing the capacitance, the resonant frequency will increase. Hence, (c) is an incorrect option.
Hence, the correct answer is (b).