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:
$\frac{1}{R_t} = \frac{1}{R_1} + \frac{1}{R_2} + ... + \frac{1}{R_n}$

We can begin by calculating the total resistance:
$\frac{1}{R_t} = \frac{1}{10} + \frac{1}{10} + \frac{1}{10}}\\\\\frac{1}{R_t} = \frac{3}{10}\\\\R_t = \frac{10}{3} = \boxed{3.333 \Omega}$

Now, we can calculate the current using Ohm's Law:
$V = iR\\\\i = \frac{V}{R}$

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

R = Resistance (Ω)

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

$i = \frac{15}{3.33} = \boxed{4.5 A}$