Question

Imagine a circuit with a 47-volt battery attached to four resistors, all in parallel: a 13-ohm resistor, a 3-ohm resistor, a 15-ohm resistor, and a 4-ohm resistor. What is the total resistance of this circuit?

Answer 1

`R_"equivalent resistance" = 1.375 Omega = 1 3/8 Omega`

Explanation:

Let's look at the current through each resistor. They all have 47 V across them so
`I_"R-13" = V/R_"13" = (47 V)/(13 Omega) = 3.615 A`

`I_"R-3" = V/R_3 = (47 V)/(3 Omega) = 15.67 A`

`I_"R-15" = V/R_"15" = 47 V/(15 Omega) = 3.133 A`

`I_"R-4" = V/R_4 = 47 V/(4 Omega) = 11.75 A`

The current out of the battery will be the sum of all those:

`I_"total" = 3.615 A + 15.67 A + 3.133 A +11.75 A = 34.17 A`

We now know the total circuit current and voltage. Ohm's Law will now tell us the circuit's equivalent resistance.

`R_"equivalent resistance" = V/I_"total" = (47 V)/(34.17 A) = 1.375 Omega = 1 3/8 Omega`

I hope this helps,
Steve