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RMS value of and current 05.06.09 By R. S. Saini (M.Sc. Physics, M.Ed.) Kendriya Vidyalaya, Sector 47, Chandigarh 9417071540

Punjab EDUSAT Society (PES) RMS value of Alternating current It is a comparison between heat produced by Alternating Current and

Punjab EDUSAT Society (PES) RMS value of Alternating Voltage

Root or R.M.S. value of Alternating voltage is defined as that value of steady Potential Difference, which would generate the same amount of heat in a given resistance is given time, as is done by A.C. voltage , when maintained across the same resistance for the same time. The R.M.S. value is also called effective value or virtual value of alternating voltage . It is

represented by VrmsPunjab, VEDUSATeff or Society Vv (PES). RMS value of Alternating current

Root or R.M.S. value of Alternating current is defined as that value of steady current, which would generate the same amount of heat in a given resistance is given time, as is done by A.C. current , when maintained across the same resistance for the same time. The R.M.S. value is also called effective value or virtual value of alternating Current . It is

represented by IrmsPunjab, I EDUSATeff or Society Iv. (PES) Expression for RMS value of Alternating current ω Let I = Io Sin t Let this current on flowing through R fo r a small time 'dt' produces a heat dH === I2 Rdt. Hence in one complete cycle (zero →→→ T ) the heat produced by A.C. is T T T H = dH = IRdt2 = IR 2 Sin 2 ωt. dt ∫0 ∫ 0 ∫ 0 0 T é1-Cos 2 ωt ù =IR2 ê ú .dt [ As 2Sin2θ= 1-Cos θ] ò0 ê ú ëPunjab2 EDUSAT û Society (PES) Expression for RMS value of Alternating current

T IR2 éT ù IR2 éSin 2 ωt ù which is = 0 ê (1-Cos2 ωt).dt ú = 0 ê t - ú ò0 ω 2ëê ûú 2ëê 2 ûú 0 éæ2.2 π ö ù 2 êç Sin .T ÷ ú 2 IRêç ÷ æSin0 ö ú IR = 0 ç T-T ÷ -ç 0 - ÷ = 0 [T].....(1) êç ω ÷ ç ω ÷ ú 2êç 2 ÷ è2 ø ú 2 êç ÷ ú ëè ø û [ Sin4π = Sin0 = 0 ]

If I v is the virtual value of A.C., then heat produced by this steady 2 current in time T is H=I V R.T …….(2) From (2) and (3) we get 2 2 2IR0 2 I 0 I 0 Iv R.T = . T or I Vvv0 = or I = or I =0 .707I 2Punjab EDUSAT 2 Society (PES)2 Expression for RMS value of Alternating Voltage On the similar lines one can calculate the RMS value of Alternating Voltage Small heat produced by Alternating Voltage 2 in small time dt is = (E 0Sin ωt) dt R on integrating it over 0 to T and equating with heat produced by DC in the same time i.e. E 2T/R we get v Eo Ev = Punjab EDUSAT Society (PES) 2