Question 11: 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 $\omega$t flowing through a wire. The effective value of the resulting current will be

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