Question

Which one of the switches, S₁, S₂ or S₃ should be opened so that:

1. total resistance is equal to 4 ohms.
2. the total resistance is equal to 3 ohms.
3. the current through 4 ohms is \[\frac{3}{5}\] th of the total current.

Answer 1

From the diagram, S₁ is in the 4 Ω branch, S₂ is in the 6 Ω branch, and S₃ is in the 12 Ω branch. Opening a switch removes that branch.

(a) Open S₁: The remaining 6 Ω and 12 Ω resistors are in parallel:

`1/R = 1/6 + 1/12`

= `3/12`

= `1/4`

R = 4 Ω

(b) Open S₂: The remaining 4 Ω and 12 Ω resistors are in parallel:

`1/R = 1/4 + 1/12`

= `4/12`

= `1/3`

R = 3 Ω

(c) Open S₃: The remaining 4 Ω and 6 Ω resistors are in parallel.

With a 24 V battery: I₄ = `24/4` = 6 A, I₆ = `24/6` = 4 A

Total current = 10 A

Thus `I_4/ I_"total" = 6/10 = 3/5`