Question

Question #210c2

Answer 1

For resistance between points `F and H`, refer to figure above.
There are three branches connected in parallel.

1. Series combination of resistors `1and2=2R`
2. Resistor `3=R`
3. Series combination of resistors `4and5=2R`

Using the parallel combination formula

`1/R_(eff)=1/(2R)+1/R+1/(2R)`
`=>1/R_(eff)=1/R((1+2+1)/2)`
`=>1/R_(eff)=2/R`
`=>R_(eff)=R/2=6.83/2=3.42\ Omega`

For resistance between points `F and G`, refer to figure above.
There are four branches connected as shown in each step.

1. Series combination of resistors `1and2=2R`
2. Above in parallel with Resistor `3=R`
   Let this be `R_1`
   We have `1/R_1=1/(2R)+1/R`
   `=>1/R_1=1/R(1/2+1)`
   `=>1/R_1=3/(2R)`
   `=>R_1=(2R)/3`
3. Series combination of resistors `R_1and5=(2R)/3+R=(5R)/3`
4. Parallel combination of above with resistor `4`.
   Using parallel combination formula we get
   `1/R_(eff)=3/(5R)+1/R`
   `=>1/R_(eff)=1/R(3/5+1)`
   `=>1/R_(eff)=8/(5R)`
   `=>R_(eff)=(5R)/8=(5xx6.83)/8=4.27\ Omega`