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I know the basic concepts about the formula and how does a voltage divider work but I can't seem to know why we should use it? Conceptually explaining why is more helpful rather than just citing practical applications about it though it can be used as a visual to provide more understanding.

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The most immediately obvious physical utility of a voltage divider is that, by adjusting the relative proportion of the two resistances (for a resistive divider), you can tone down the voltage to any number ranging from zero, to a maximum = voltage value you feed into the divider arrangement.

Since $$V_{\rm (across \ R_2)} = V_{\rm (applied)} \left( \frac{R_2}{R_1 + R_2} \right)$$ Now imagine, if we keep vary $R_1$ and $R_2$ in a manner such that their sum is kept the same (e.g. the combinations [$1k, 9k$], [$2k, 8k$], [$3k, 7k$] etc.), in each case, voltage across $R_2$ is also changing in steps of $V_{\rm applied}/10$. The step size can always be altered, simply by changing the relative proportion.

Now. if this voltage across $R_2$ is passed onto some secondary circuit, you have complete control over the voltage that drives the other circuit (through the resistance proportion). Thus, you can influence the output of the secondary circuit simply by controlling this relative proportion of resistances.

The applications of this idea can be diverse - from creating a variable voltage supply from a fixed high voltage, to practical stuff like regulators for appliances (e.g. take a fan, passing lesser voltage/power, implies that the output is toned down proportionately, fan speed can be controlled). In circuitry, you need this as an important circuit component, to give calculated voltage biases, such as in a voltage comparator circuit using an operational amplifier (one of the many possible applications) and in generating timing waveforms (using e.g. an astable multivibrator). Dividers are also important parts of the circuit in digital-analog conversion circuits (which make use of voltage-divider ladder circuits) etc. There can be more sophisticated applications too (which probably your book has listed.)

In each case, the basic idea remains the same. Controlling voltage by adjusting the relative proportion of resistances.

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  • $\begingroup$ Your answer complimented to what I was thinking about dividers and somewhat gave me answers and I've read somewhere in a forum that using dividers are risky? or wasteful because it explained that if given a situation where there are two resistors R1 and R2. R1 being the closest to the positive terminal, and has a resistance much much larger than R2. It will have a tendency to heat-up and blow out or melt. Therefore, wasting energy and such. Is this true? and if yes, why are we still considering a voltage divider as an accepted example in physics if it is that wasteful or will be seldom used? $\endgroup$ – Czar Luc Mar 11 '17 at 14:34
  • $\begingroup$ @CzarLuc - Could you please point me towards the source of that statement? "Risky" could be context specific. It is certainly not a wasteful example as far as I can guess, but maybe in some context, there was some specific drawback. $\endgroup$ – 299792458 Mar 11 '17 at 14:37
  • $\begingroup$ The "risky" would be the part of heating or melting in the resistor R1. Since heating up and melting of resistors might cause accidents. Sorry if I did not point that out. $\endgroup$ – Czar Luc Mar 11 '17 at 14:40

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