Question

What is the voltage drop across the entire parallel portion of the circuit?

Answer 1

Given:

The value of each of the parallel resistances is,

$60\text{ ohm}$

The resistance in series with it is,

$30\text{ ohm}$

The potential difference across the combination is,

$V=120\text{ V}$

To find:

The potential drop across the parallel portion

Explanation:

The circuit diagram looks like:

The equivalent resistance of the circuit is,

$\begin{gathered} R=30.0+(60.0\parallel60.0) \\ =30.0+\frac{60.0\times60.0}{60.0+60.0} \\ =30.0+30.0 \\ =60.0\text{ ohm} \end{gathered}$

The current through the circuit is,

$\begin{gathered} i=\frac{V}{R} \\ =\frac{120}{60.0} \\ =2.0\text{ A} \end{gathered}$

The potential drop across 30.0 ohm is,

$\begin{gathered} V_{30.0}=i\times30.0 \\ =2.0\times30.0 \\ =60\text{ V} \end{gathered}$

The potential drop across the rest parallel portion is,

$\begin{gathered} V_{rest}=V-V_{30.0} \\ =120-60 \\ =60\text{ V} \end{gathered}$

Hence, the voltage drop across the entire parallel portion is 60 V.