Question

Apply: what will be the total resistance and current in a parallel circuit with a 15-volt battery and three 10-ohm resistors? test your answers with the gizmo.

Answer 1

1) Total resistance

the total resistance of a circuit with n resistors in parallel is given by

`(1)/(R_(eq)) = (1)/(R_1)+ (1)/(R_2)+...+ (1)/(R_n)`
where
`R_i` are the single resistances.

In our circuit, we have 3 resistors of
`10.0 \Omega` each, so the total resistance of the circuit is given by

`(1)/(R_(eq))= (1)/(10 \Omega)+ (1)/(10 \Omega)+ (1)/(10 \Omega)= (3)/(10 \Omega)`
which means a total resistance of

`R_(Eq) = (10 \Omega)/(3)=3.33 \Omega`

2) Current in the circuit

The current in the circuit can be found by using Ohm's law:

`I= (V)/(R_(Eq))`
where V is the voltage of the battery and Req is the total resistance we found before. By using V=15 V, we find

`I= (15 V)/(3.33 \Omega)=4.5 A`