Suppose a student is trying to make a measurement system named mach system, so that he can use it like a code measurement system. If he takes unit of mass as A kg, the unit of length as B meter, the unit of time as C second and the unit of charge as d coulomb.In mach system, 1 ohm isIn mach system, 1 farad is

The dimensions of resistance are I−2ML2T−3,where I is electric current.∴ Q=ItWhere Q is electric charge.∴ [Q]=[IT]⇒[I]=QT−1Dimensions of resistance are Q−2ML2T−1∵     n1U1=n2U2 or  1Q1-2M1L12T1−1=n2Q2-2M2L22T2−1∴ n2=Q1Q2−2M1M2L1L22T1T2−1  =Q1Q1d−2M1AM1L1BL12T1CT1−1 =A−1B−2Cd−2Farad is SI unit of capacitance of capacitor, its dimensions areI2M−1L−2T4=Q2M−1L−2T2∴ n1v1=n2v2 or  1Q12M1−1L1−2T12=n2Q22M2−1L2−2T22∴ n2=Q1Q22M1M2−1L1L2−2T1T22=Q1Q1d2M1AM1−1L1BL1−2T1CT12=d−2AB2C−2