Question

Find the value for the voltage drop across each 15 Ohm resistor

Answer 1

Given:

The value of each resistance in parallel combination is,

$15.0\text{ ohm}$

The value of the resistance in series with the parallel resistances is,

$10.0\text{ ohm}$

The potential drop across the battery is,

$45.0\text{ V}$

To find:

The voltage drop across each 15.0 ohm resistance

Explanation:

The value of the equivalent resistance of the three parallel resistances is,

$\begin{gathered} \frac{1}{R}=\frac{1}{15.0}+\frac{1}{15.0}+\frac{1}{15.0} \\ \frac{1}{R}=\frac{3}{15.0} \\ R=\frac{15.0}{3} \\ R=5.0\text{ ohm} \end{gathered}$

The net resistance of the circuit is,

$\begin{gathered} R_{net}=10.0+5.0 \\ =15.0\text{ ohm} \end{gathered}$

The circuit diagram is like this:

The current in the circuit is,

$\begin{gathered} I=\frac{V}{R_{net}} \\ =\frac{45.0}{15.0} \\ =3.0\text{ A} \end{gathered}$

The potential drop across 10.0 ohm is,

$\begin{gathered} I\times10.0 \\ =3.0\times10.0 \\ =30.0\text{ V} \end{gathered}$

The potential drop across each of the 15.0 ohm resistance will be the same as the resistances are parallel.

So, the potential drop across each 15.0 ohm is,

$\begin{gathered} 45.0-30.0 \\ =15.0\text{ V} \end{gathered}$

Hence, the required potential drop is 15.0 V.