Are a Battery's EMF and Terminal Voltage the Same?

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A battery's electromotive force (emf) represents the maximum energy supplied per coulomb of charge, while terminal voltage is the actual voltage available at the battery's terminals. The difference arises due to internal resistance; when current flows, some emf is lost as voltage drop across this resistance. Terminal voltage equals emf only when no current flows, as there are no 'lost' volts. Conversely, during a short circuit, all emf is dropped across internal resistance, resulting in zero terminal voltage. Understanding this distinction is crucial for evaluating battery performance in various applications.
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How are a battery's emf and its terminal voltage different? Can they ever be the same value?
 
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A battery's emf is the maximum energy supplied to each coulomb of charge passing through the battery. A battery (and other sources for that matter) have internal resistance. When a current flows, some of the supply's emf is 'lost' as V = Ir where r is the internal resistance. These 'lost' volts aren't available to the terminals, therefore terminal voltage is 'lost' volts subtracted from the emf. Terminal voltage and emf have the same value when no current flows in a circuit as no volts will be 'lost'. On the other hand, when a source is short-circuited there is no external resistance (load) so all the emf is dropped across the internal resistance, and thus the entire emf becomes 'lost' volts and there is zero terminal voltage.
 
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thank you this is a great explanation
 

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