The equivalent resistance R of two resistances connected in parallel is given by $\frac { 1 } { R } = \frac { 1 } { R _ { 1 } } + \frac { 1 } { R _ { 2 } }$ . Find the equivalent resistance for two resistances of 50 ? and 30 ? connected in parallel.
A) R = 23.8 ?
B) R = 18.8 ?
C) R = 16.8 ?
D) R = 40 ?
E) R = 19.2 ?

Question

The equivalent resistance R of two resistances connected in parallel is given by $\frac { 1 } { R } = \frac { 1 } { R _ { 1 } } + \frac { 1 } { R _ { 2 } }$ . Find the equivalent resistance for two resistances of 50 ? and 30 ? connected in parallel.
A) R = 23.8 ?
B) R  = 18.8 ?
C) R  = 16.8 ?
D) R  = 40 ?
E) R  = 19.2 ?

Quizplus · Accepted Answer

The equivalent resistance $ R $ for two resistances $ R_1 = 50 \, \Omega $ and $ R_2 = 30 \, \Omega $ in parallel is calculated as follows:  $\frac{1}{R} = \frac{1}{50} + \frac{1}{30} = \frac{3}{150} + \frac{5}{150} = \frac{8}{150}$  Thus, $ R = \frac{150}{8} = 18.75 \, \Omega $, which rounds to 18.8 \, \Omega.

The Equivalent Resistance R of Two Resistances Connected in Parallel 1R=1R1+1R2\frac { 1 } { R } = \frac { 1 } { R _ { 1 } } + \frac { 1 } { R _ { 2 } }R1​=R1​1​+R2​1​

The Equivalent Resistance R of Two Resistances Connected in Parallel $\frac { 1 } { R } = \frac { 1 } { R _ { 1 } } + \frac { 1 } { R _ { 2 } }$