Chapter 27, Problem 79A

To determine

To Calculate: The total load in amperes.

Answer to Problem 79A

  $10\text{A}$

Explanation of Solution

Given data:

  $12$ Sets of bulbs at $120\text{V}$

Each set: $24$ bulbs, Series, R $=6\Omega$

All sets operated from single outlet.

Formula used:

Equivalent resistance:

In series, $R_{Total}={\displaystyle \sum R_i}$

In parallel, $\frac{1}{R_{Total}}={\displaystyle \sum \frac{1}{R_i}}$

As per Ohm’s law:

  $V=I\times R$

Here, I is the current and R is the resistance.

Calculation:

  $\to$For single set

Resistance of each bulb $=6\Omega$

Number of bulbs $=24$

Total resistance of each set

  $\begin{array}{l}=24\times 6\\ =144\Omega \end{array}$

As, all sets are operated from single outlet, all sets are in parallel.

  $\to$ Total resistance of 12 sets in parallel

  $\frac{1}{R_T}={\displaystyle \sum _{}^{12}\frac{1}{144}}$

  $R_T={\left(\frac{12}{144}\right)}^{-1}$

  $R_T=12\Omega$

Load in amperes can be calculated using Ohm’s law:

  $\to$$V=IR$

  $\begin{array}{l}V=120\text{V}\\ R=12\Omega \end{array}$

  $\begin{array}{l}I=\frac{120}{12}\\ I=10\text{A}\end{array}$

Conclusion:

The total load is $10\text{A}$ .