A field communications transceiver is powered by a battery string consisting of 7 series-c… — Armed Services Vocational Aptitude Battery (ASVAB)

A field communications transceiver is powered by a battery string consisting of 7 series-connected cells. Six of the cells each supply an electromotive force (EMF) of $2.4\text{ V}$ in a series-aiding configuration, while one $2.4\text{ V}$ cell is connected in series opposing. What is the net electromotive force, in volts ( $\text{V}$ ), delivered by the battery string?

Answer: 12 V

Answer

The net electromotive force delivered by the battery string is

12\text{ V}

In a series circuit, aiding EMFs add together while opposing EMFs subtract:

V_{\text{net}} = (6 \times 2.4\text{ V}) - (1 \times 2.4\text{ V}) = 14.4\text{ V} - 2.4\text{ V} = 12.0\text{ V}

Step-by-Step Solution

Calculate the total electromotive force contributed by the series-aiding cells.

6 \times 2.4\text{ V} = 14.4\text{ V}

When cells are connected in series aiding (the positive terminal of one connected to the negative terminal of the next), their voltages add together directly.

Subtract the electromotive force of the series-opposing cell from the aiding total.

14.4\text{ V} - 2.4\text{ V} = 12.0\text{ V}

A cell connected in reverse polarity opposes the circuit electromotive force, subtracting its potential difference from the total.

Key Concept

Series electromotive force addition and subtraction: aiding cells add potential (

+V

), whereas opposing cells subtract potential (

-V

Alternative Method

Find the effective number of aiding cells:

6 - 1 = 5

net aiding cells. Then calculate net voltage:

5 \times 2.4\text{ V} = 12.0\text{ V}

Estimated Time:45s

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