Question

What will be the total resistance and current in a parallel circuit with a 15-volt battery and three 10-ohm resistors?

Answer 1

Hello!

Recall for resistors in parallel:

`(1)/(R_t) = (1)/(R_1) + (1)/(R_2) + ... + (1)/(R_n)`

We can begin by calculating the total resistance:

`(1)/(R_t) = (1)/(10) + (1)/(10) + (1)/(10)}\\\\(1)/(R_t) = (3)/(10)\\\\R_t = (10)/(3) = \boxed{3.333 \Omega}`

Now, we can calculate the current using Ohm's Law:

`V = iR\\\\i = (V)/(R)`

V = Voltage of battery (V)
i = Current (A)

R = Resistance (Ω)

Plug in the given voltage and the total resistance we solved for.

`i = (15)/(3.33) = \boxed{4.5 A}`