Answer to Question #147502 in Electric Circuits for Milo

Question

The P.D.across the resistor is 160V and that of across the inductor is 120V .Find the effective value of the applied voltage.When these are connected across an a.c.source. If the effective current in the circuit be 1A calculate the impedance.

Answer 1

$I =1.0A\space as\space given\\ V_R=160V=IR R=I\times R 1\times 160=160\\ V_L=120V=IR R=I\times R 1\times 120=120\\ V_{net}= \sqrt {V ^{2}{_R}+ {V ^{2}{_L} }}\\ \qquad=\sqrt {160 ^{2}+ {120 ^{2}}}\\ \qquad=\sqrt {25600+ 14400}\\ \qquad =\sqrt {40000}\\ \qquad=200\\ \qquad effective \space value\space of \space applied\ voltage=200\\ Z= \sqrt {R ^{2}+ {L^{2} }}\\ \qquad = \sqrt {160 ^{2}+ {120^{2} }}\\ \qquad=\sqrt {25600+14400}\\ \qquad=\sqrt {40000}\\ \qquad=200\\ impedance=200$