Evaluate the Solution You and your friend are studying for the next physics exam

Question

Evaluate the Solution You and your friend are studying for the next physics exam by working through some problems. Given the diagram below, where R_1 = 5 Ohm, R_2 = 10 Ohm, R_3 = 20 Ohm, you are supposed to find the total resistance between points A and B. Your friend comes up with the following solution: R_tot -1/(R_1 + R_2) + 1/R_3 = 1/(5 Ohm + 10 Ohm) + 1/20 Ohm = 0.177 Ohm Do you think your friend's solution is correct? Justify your answer with as many supporting arguments as possible. Use words, pictures, diagrams, and equations in your arguments.

Explanation / Answer

Give circuit diagram

   R1= 5 ohm, R2 = 10 ohm , R3 = 20 ohm

here

   R1,R2 are in series so the resultant resistance of R1,R2 is

   R1,2 = R1+R2 = 5 ohm + 10 ohm = 15 ohm

and R3 is in parallel combination with R1,2 so the equivalent resistance (R) of the circuit is

   1/R = 1/R1,2 + 1/R3

   1/R = 1/15 +1/20

solving for R

   R = 8.57143 ohm

i will not agree with my friend's solution , the mistake is 1/R1+1/R2 it should R1+R2

so the finally the solution is

   1/R = (1/(R1+R2) + 1/R3)

   = (1/(5+10) +1/20)

   = 1/15 +1/20

   R = 8.57143 ohm

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