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The question arises from the fact the voltage provided across battery terminals is constant no matter how much current is drawn (for non-ideal batteries the current draw is limited but still can be varied over a range).

EDIT: Voltage is basically the potential difference or the energy required to displace a charge against the electric field. Therefore, voltage causes charges to move from one terminal of the battery to other. Now if the voltage is constant then you must be able to move only a constant number of charges per second (current). What follows from this is that if I have a higher voltage I should be able to move higher number of charges.

Now, if voltage causes current to flow then a 9 V battery should always supply a fixed amount of current but this is not true!

So, does voltage actually have a direct influence over the current? If yes, How would you explain the case of a battery which can provided a range of currents for a constant voltage? If no, what would a better way to think about voltage apart from the fallacious "voltage causes current to flow" statement.

(Sidenote: I feel like the statement "voltage causes current to flow" is an over generalisation of the concept. This over generalisation causes an information gap while explaining the phenomenon. Would you agree?)

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For an ideal battery it is indeed true that the potential difference across its terminals is constant, which means that a fixed amount of energy is transferred per coulomb of charge that flows through any device connected across its terminals.

This doesn't imply that any charge will flow. For example if nothing is connected to the battery, there is air between the terminals and the current (rate of flow of charge) will be zero! If 1 M$\Omega$ resistor is connected across the terminals of a 1.5 volt cell, there will be a current of 1.5 $\mu$A; for a 10 $\Omega$ resistor the current will be 0.15 A, and so on. The current depends, then, on the device connected across the terminals and not just on the battery voltage.

However, for a given simple conductor, the bigger the voltage we apply across it, the greater the current. For metals and most pure materials, the current is proportional to the voltage (Ohm's Law) provided that the temperature (and, strictly speaking, other external conditions) stay constant. This does not follow from the definition of voltage as a matter of simple logic, instead its justification requires understanding of charge transport mechanisms in particular materials. If there were a purely logical argument for Ohm's law following from definitions of voltage and current alone, the law would apply to all conductors, but it doesn't!

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  • $\begingroup$ “However, for a given device, the bigger the voltage we apply across it, the greater the current.” This is not generally true. There are simple counter examples like a capacitor in steady state, as well as more complicated counter examples like a regulated current supply within its design limits, which is designed specifically to produce a constant current regardless of the supply voltage. $\endgroup$
    – Dale
    May 16, 2020 at 13:27
  • $\begingroup$ @Dale Thanks. "Device'" was the wrong word to have chosen. $\endgroup$ May 16, 2020 at 13:46
  • $\begingroup$ Good revision. +1 $\endgroup$
    – Dale
    May 16, 2020 at 13:47
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For an ideal (zero internal resistance) battery the voltage across its terminals is constant and equals its internal Emf, regardless of the current it delivers. For a real battery with internal resistance $r_b$ it is not. However for a range of load resistance $R_L$ where $R_{L}>>r_b$ then the terminal voltage will be constant and equal its Emf regardless of the current.

The terminal voltage is

$$V_{T}=Emf-Ir_b$$

The current in the circuit is

$$I=\frac{Emf}{R_{L}+r_b}$$

Then, for all $R_{L}>>r_b$, $I=\frac{Emf}{R_L}$ and thus $ V_{T}=Emf$

Hope this helps.

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Now, if voltage causes current to flow then a 9V battery should always supply a fixed amount of current but this is not true!

Your reasoning is sound, and as you correctly point out the conclusion is false. Therefore you know that the premise must be false.

In fact, voltage does not generally cause current to flow. In a capacitor you can have voltage with no current and in an inductor you can have current with no voltage. Active circuit elements similarly do not have a “voltage causes current” relationship.

Some circuit elements do have a “voltage causes current” relationship, most notably resistors. However, this relationship is not a general rule of nature, it is a defining characteristic of specific materials and does not apply to other materials.

If no, what would a better way to think about voltage apart from the fallacious "voltage causes current to flow" statement.

A better way to think is to recognize that every circuit element enforces its own relationship between voltage and current. There isn’t an easy “sound bite” summary. You have to learn every different relationship and recognize that the relationship is fundamentally different for each type of circuit element.

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