Examkin

Question

Difficulty: HardVoltage and Electromotive Force (EMF)

An aircraft instrumentation circuit incorporates a 24 V24\text{ V} primary DC power source connected in series-aiding polarity with a 750 mV750\text{ mV} reference cell. If a 1.75 V1.75\text{ V} auxiliary bias source is wired into the same series branch in series-opposing polarity, what is the net electromotive force (EMF) measured across the output terminals?

  1. A
    26.5 V26.5\text{ V}
  2. 23.0 V23.0\text{ V}Answer
  3. C
    772.25 V772.25\text{ V}
  4. D
    23.0 A23.0\text{ A}

Answer

The net electromotive force across the terminals is 23.0 V23.0\text{ V}.
The correct answer is obtained by converting 750 mV750\text{ mV} to 0.75 V0.75\text{ V}, summing the aiding sources (24 V+0.75 V=24.75 V24\text{ V} + 0.75\text{ V} = 24.75\text{ V}), and subtracting the opposing 1.75 V1.75\text{ V} source, resulting in a net electromotive force of 23.0 V23.0\text{ V}.

Step-by-Step Solution

1
Convert the reference cell rating from millivolts to volts
750 mV=750×10−3 V=0.75 V750\text{ mV} = 750 \times 10^{-3}\text{ V} = 0.75\text{ V}
All voltage values in a series combination must be expressed in the same unit before performing arithmetic operations.
2
Combine the series-aiding electromotive forces
Vaiding=24 V+0.75 V=24.75 VV_{\text{aiding}} = 24\text{ V} + 0.75\text{ V} = 24.75\text{ V}
Voltage sources connected in series-aiding polarity reinforce one another, so their potentials add directly.
3
Subtract the series-opposing bias source to find the net EMF
EMFnet=24.75 V−1.75 V=23.0 V\text{EMF}_{\text{net}} = 24.75\text{ V} - 1.75\text{ V} = 23.0\text{ V}
A source wired in opposing polarity establishes a potential in the reverse direction, reducing the overall electromotive force.

Key Concept

Series electromotive force calculation involving aiding/opposing polarities and metric prefix conversion
Estimated Time:1m 15s
Rate this question

Topics

Voltage and Electromotive Force (EMF)

More questions from this topic