SOLUTION

To take care of change in frequency of the A.C current, while using a moving iron type instrument a condenser of suitable value is used in parallel with the swamp resistance.

Error due to changes in frequency: In certain types of instruments, like in moving iron instruments, the change in frequency causes an error due to the change in magnitude of eddy currents set up in the metal portion of the instruments. Changes in frequency cause changes in reactance of the operating coil (X = 2πf ).  At high frequencies, the meter will give a reading lower than the actual value and vice-versa. This type of error can be eliminated only if the impedance of the coil is independent of the frequency. This is achieved by having a capacitance in shunt with the swamping resistance of the coil as shown in Fig. 

As shown in Fig. let R and L be the resistance and inductance of the coil of the moving-iron instrument and let r(R>>r) be the swamping resistance connected in series to eliminate the temperature errors. Let C be the values of the capacitance to be shunt-connected so that the impedance remains unaltered. Then, the total impedance Z which remains independent of the frequency is given as

If Z is to be independent of the frequency, then it must not contain any j terms or the j terms should be equal to zero.i.e

But generally

(ωCr)² << 1

∴ ω − ωCr² = 0

C = L/r²