Work is done to push electrons from the positive to the negative terminal. The work done per unit charge is known as the electromotive force, or emf:

$$ε = emf = W/q$$A battery converts chemical energy into electrical energy to do work in driving elections around a circuit. Inside the battery, work is done to drive electrons from the positive to the negative terminal, which the current is said to travel from the negative to the positive terminals. Hence work is done on the electrons. The force involved is known as the electromotive force, emf.

A battery cannot pass electrons through its electrolyte without loss of energy due to resistance. This is the battery's internal resistance, r, and can be assumed to be in series with the cell. The current I that leaves the battery times the internal resistance is the voltage V of the battery:

$$V = ε - Ir$$where V is the voltage supplied by a battery with emf (electromagnetic force) ε, I the current, and r its internal resistance.

When loads are in series, the same current must pass through all of them. Since the voltage across all the resistors is the voltage of the circuit:

$V = IR_{tot} = I(R_1 + R_2 + R_3 + ..)$, so:

$$R_{total} = R_1 + R_2 + R_3 +....$$where $R_{tot}$ is the total resistance of individual resistances $R_1, R_2, R_3 ....$ arranged in series.

When loads are in parallel, the current is split up into the different branches of the circuit, but the voltage is the same across each branch:

$V/{R_{tot}} = I_{tot} = V/{R_1} + V/{R_2} + V/{R_3} + ...$, so:

$$1/{R_{tot}} = 1/{R_1} + 1/{R_2} + 1/{R_3} +...$$where $R_{total}$ is the total resistance of individual resistances $R_1, R_2, R_3 ....$ arranged in parallel.

Current is measured by an instrument called the ammeter, named after André-Marie Ampère (1775–1836), a French scientist who pioneered work in electrodynamics. The ammeter has a small electrical resistance, but an *ideal ammeter* has zero resistance. In practice, ammeters will consume a small amount of the power of a circuit, but this is usually considered as negligible for the purpose of calculations.

Potential difference, or voltage, is measured by an instrument called the voltmeter, named after Alessandro Volta (1745–1827), an Italian scientist who made the first wet cell battery, and solved the controversy of the nature of animal electricity. The voltmeter has a large electrical resistance, but an *ideal voltmeter* has infinite resistance. In practice, voltmeters will draw a small amount of power from the main circuit, but this is usually considered as negligible for the purpose of calculations.

A galvanometer is a device used for detecting electric current. It is the basis of both the voltmeter and the ammeter. It has a coil which causes a rotation of a pointer when an electric current passes through it due to the induced magnetic field.

A voltmeter is attached in parallel to a section of a circuit. It consists of a galvanometer in series with a very high resistance (at least 50kΩ). The high resistance ensures that very little current is drawn out of a circuit when the voltmeter is connected in parallel. The reading on the voltmeter is a measure of the potential difference across the resistance (V = IR).

An ammeter is an instrument positioned in series within a circuit. Its galvanometer is in parallel with the ammeter's very low resistance, so that little current passes through the galvanometer directly, but allows the current to create torque on the dial to display the current's magnitude and direction.

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1744 - 1807

Johann Bernoulli (III) lived and worked in Berlin, where he was director of the Mathematics Department of the Academy of Berlin, and the last noted mathematician of the Bernoulli dynasty of mathematicians.

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