Question

Find the equivalent resistance (detailed solution)

Answer 1

Answer

3

Left resistance

These three resistances are in Parallel. Their fractions are added.

• 1/4 + 1/6 + 1/12 = 1/R_left           Make everything out of 12s
• 3/12 + 2/12 + 1/12 = 1/R_left      Add  
• 6/12 = 1/R_left                           Reduce
• 1/2 = 1/R_left                             Cross Multiply
• 1*R_left = 2                                Simplify
• R_left = 2                                  Answer for left

Right Resistance

• 1/2 + 1/2 = 1/R_right                 Add reciprocals
• 2/2 = 1/R_right                        Simplify  
• 1 = 1/R_right                             Multiply both sides by R_right
• R_right = 1

Answer

R_left + R_right = 2 + 1 = 3