question_answer

In the given electric circuit if the current flowing through \[3\,\Omega \] resistor is 1 A, find the voltage of the battery and the current I drawn from it.

Answer:

\[{{R}_{2}}=3\,\Omega \]

\[{{I}_{2}}\,=1\,A\]

\[{{V}_{2}}={{I}_{2}}\,{{R}_{2}}=1\times 3=3\,volts\]

Resultant of \[{{R}_{2}}\] and \[{{R}_{3}}\] is R?.

\[\frac{1}{R'}=\frac{1}{{{R}_{2}}}+\frac{1}{{{R}_{1}}}=\frac{1}{3}+\frac{1}{6}=\frac{2+1}{6}=\frac{3}{6}=\frac{1}{2}\]

\[R'=2\,\Omega \]

\[{{V}^{'}}={{V}_{2}}=3\,volts\]

\[I'\,=?\]

\[I'=\frac{V'}{R'}=\frac{3}{2}A=1.5A\]

\[I\text{ }=I=1.5A\]

Resultant resistance in the circuit = R

\[R={{R}_{1}}+R'=2+2=4\Omega \]

\[I=\frac{3}{2}A\]

\[V=?\]

\[V=IR=\frac{3}{2}\times 4=volts\]

\[\Rightarrow \]     E = 6 volts