Question

When two resistors are wired in series with a 12 V battery, the current through the battery is 0.30 A. When they are wired in parallel with the same battery, the current is 1.6 A. What are the values of the two resistors?

Note: I understand other people have asked the same concept with different numbers, and their questions have been answered, however I do not understand why you need to multiple R1 by R2 when the resistors are in parallel, and furthermore, why are you supposed to multiply the "in parallel" equation by (R1+R2; the in series resistors) to find R1*R2?

Answer 1

`30\Omega, 10\Omega`

Step-by-step explanation:

Let two resistors R1 and R2 are wired in series.

Potential difference, V=12 V

Current=I=0.3 A

We have to find the value of two resistors.

When two resistors are connected in series

`R=R_1+R_2`

`V=IR=I(R_1+R_2)`

Substitute the values

`12=0.3(R_1+R_2)`

`R_1+R_2=(12)/(0.3)=40`

`R_1+R_2=40`..(1)

In parallel

`(1)/(R)=(1)/(R_1)+(1)/(R_2)`

`(1)/(R)=(R_2+R_1)/(R_1R_2)`

`R=(R_1R_2)/(R_1+R_2)`

Current in parallel, I=1.6 A

`V=IR`

`V=1.6((R_1R_2)/(R_1+R_2))`

`(12)/(1.6)=(R_1R_2)/(40)`

`R_1R_2=(12* 40)/(1.6)=300`

`R_1-R_2=√((R_1+R_2)^2-4R_1R_2)`

`R_1-R_2=√((40)^2-4(300))=20`....(2)

Adding equation (1) and (2)

`2R_1=60`

`R_1=(60)/(2)=30\Omega`

Substitute the value in equation (1)

`30+R_2=40`

`R_2=40-30=10\Omega`