Question 12: AC fundamentals

Question

A direct current of 6 A is superimposed on an alternating current I = 10 sin $\omega$t flowing through a wire. The effective value of the resulting current will be

Accepted Answer

Given, $I = 6 + 10\sin \omega t$
${I_{eft}} = \left[ {{{\int\limits_0^T {{I^2}dt} } \over {\int\limits_0^T {dt} }}} ight] = {\left[ {{1 \over T}\int\limits_0^T {{{(6 + 10\sin \omega t)}^2}dt} } ight]^{1/2}}$
$ = {\left[ {{1 \over T}\int\limits_0^T {(36 + 120\sin \omega t + 100{{\sin }^2}\omega t)dt} } ight]^{1/2}}$
But as, ${1 \over T}\int\limits_0^T {\sin \omega t\,dt = 0} $ and ${1 \over T}\int\limits_0^T {{{\sin }^2}\omega t = {1 \over 2}} $
$ \Rightarrow {I_{eff}} = {\left[ {36 + {1 \over 2} 	imes 100} ight]^{1/2}} = 9.27$
Thus, ${I_{eff}} = 9.27\,A$

Answer

5$\sqrt2$

Answer

5$\sqrt3$

Answer

9.27

Answer

8.37

AC fundamentals

A direct current of 6 A is superimposed on an alternating current I = 10 sin \omegat flowing through a wire. The effective value of the resulting current will be

Choose the correct answer: