question_answer

In the circuit given E = 6.0 V, R1 = 100 ohms, R2 = R3 = 50 ohms, R4 = 75 ohms. The equivalent resistance of the circuit, in ohms, is                                                                          [KCET 2005]

A)         11.875

B)         26.31

C)         118.75

D)         None of these

Correct Answer: C

Solution :

                                         In given circuit three resistance \[{{R}_{2}},{{R}_{4}}\] and \[{{R}_{3}}\] are parallel.                    \[\frac{1}{R}=\frac{1}{{{R}_{2}}}+\frac{1}{{{R}_{4}}}+\frac{1}{{{R}_{3}}}\]                    \[=\frac{1}{50}+\frac{1}{50}+\frac{1}{75}\]                    \[=\frac{75+75+50}{50\times 75}\]                    \[R=\frac{50\times 75}{75+75+50}=\frac{50\times 75}{200}=\frac{75}{4}\Omega =18.75\Omega \]                    This resistance is in series with \[{{R}_{1}}\]                                                    \ \[{{R}_{\text{resultant}}}={{R}_{1}}+R=100+18.75=118.75\Omega \]