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Zorluk: Çok zorVoltage and Electromotive Force (EMF)

A technician is constructing a series battery bank using standard 1.5 V1.5\text{ V} cells. During the assembly process, they accidentally reverse the polarity of exactly two cells. When they measure the total electromotive force (EMF) across the completed battery bank, the multimeter reads 15 V15\text{ V}. How many total cells are in the battery bank?

  1. A
    8 cells
  2. B
    10 cells
  3. C
    12 cells
  4. 14 cellsCevap

Cevap

The battery bank contains 14 cells.
The total electromotive force (EMF) of a series circuit is the algebraic sum of the individual cell voltages. A correctly oriented cell adds 1.5 V1.5\text{ V}, while a reversed cell subtracts 1.5 V1.5\text{ V}. Each reversed cell not only fails to add its voltage but actively opposes the other cells, effectively reducing the total maximum potential by 3.0 V3.0\text{ V} per reversed cell. To find the total number of cells (NN), we use the equation: Vtotal=(Nforward×1.5 V)−(Nreversed×1.5 V)V_{\text{total}} = (N_{\text{forward}} \times 1.5\text{ V}) - (N_{\text{reversed}} \times 1.5\text{ V}). Given 15 V15\text{ V} total and 2 reversed cells, the equation becomes 15=(N−2)(1.5)−(2×1.5)15 = (N - 2)(1.5) - (2 \times 1.5). Solving this gives 15=1.5N−615 = 1.5N - 6, which results in 1.5N=211.5N = 21, meaning N=14N = 14 cells.

Adım Adım Çözüm

1
Identify the formula for the total voltage of cells in series when some are reversed.
Vtotal=(Nforward×1.5 V)−(Nreversed×1.5 V)V_{\text{total}} = (N_{\text{forward}} \times 1.5\text{ V}) - (N_{\text{reversed}} \times 1.5\text{ V})
Reversed cells subtract their voltage from the total EMF instead of adding to it.
2
Express the number of forward cells in terms of the total number of cells (NN).
Nforward=N−2N_{\text{forward}} = N - 2
The total number of cells is the sum of forward-facing and reversed cells, and we know exactly 2 are reversed.
3
Substitute the known values into the voltage equation and solve for NN.
15=(N−2)(1.5)−(2×1.5)15 = (N - 2)(1.5) - (2 \times 1.5)
This sets up the algebraic equation to find the total number of cells.
4
Simplify and solve the equation for NN.
15=1.5N−3−3  ⟹  15=1.5N−6  ⟹  21=1.5N  ⟹  N=1415 = 1.5N - 3 - 3 \implies 15 = 1.5N - 6 \implies 21 = 1.5N \implies N = 14
Solving the equation reveals that 14 total cells are required to produce a 15 V15\text{ V} output with 2 reversed cells.

Anahtar Kavram

Series Voltage Summation and Polarity
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Konular

Voltage and Electromotive Force (EMF)

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