If the emf of an AC source is given by 6 t+4 2 t ~V , then the rms value of the emf is

Step-by-step solution

Given, emf of an AC source, aligned & E=6 t+4 2 t & Now, E^2=(6 t+4 2 t)^2 & E^2=36 ^2 2 t+16 ^2 2 t+48 t 2 t & =36 ^2 t+16 ^2 2 t+48 ( t 2 - 3 t 2 ) aligned Now, the average value of E^2 , aligned & E_ avg = 1 T ₀^T [E^2 d t ] & = 1 T ₀^T [36 ^2 t+16 ^2 2 t+48 ( t 2 - 3 t 2 ) ] & = 1 T [36 T 2 +16 T 2 +48(0-0) ] & or E_ avg =18+8=26 ~V & E_ rms = E_ avg = 26 ~V & aligned So, the rms value of emf is 26 ~V .