A battery has an emf of 15.0 V. The terminal voltage of the battery is 11.6 V when it is deliver

A battery has an emf of 15.0 V. The terminal voltage of the...

Key Concepts

Electrical Power in Resistive Circuits

Electrical power in resistive circuits is the rate at which electrical energy is converted to heat or work in a resistor. It is calculated using formulas that relate power to voltage and resistance, such as P = V²/R, and is essential for analyzing energy consumption and conversion in circuits.

Ohm's Law

Ohm's Law is a fundamental principle in electronics which states that the voltage across a resistor is directly proportional to the current flowing through it, with the constant of proportionality being the resistance. It is used to determine unknown quantities like current or resistance in a circuit.

Terminal Voltage

Terminal voltage is the voltage output of a battery measured across its terminals when it is delivering current to a load. It is affected by the internal resistance of the battery and is generally lower than the electromotive force under load conditions.

Internal Resistance

Internal resistance is the inherent resistance within a power source that causes a voltage drop as current flows. It represents energy losses inside the source and results in the terminal voltage being lower than the electromotive force when a load is connected.

Electromotive Force (EMF)

EMF is the energy provided per unit charge by a power source in an electrical circuit, typically represented by a battery. It is the open-circuit voltage of the device and reflects the maximum potential difference available before any internal losses occur.

Transcript

00:01 So for this problem, we have a battery source or voltage source connected to a resistor, and current sort of just flows in the circuit, assuming it's completed.

00:18 Now, it says that the battery has an emf or electromotive force of 15 volts.

00:25 Think of that as sort of the ideal voltage that can be supplied from this battery or, yeah, it's a battery in this case.

00:34 However, it tells us that there is only 11 .6 voltage between the terminals.

00:46 So essentially, this is the sort of the peer value of what the battery can supply, but this is actually what it's supplying.

00:53 Maybe it's old, maybe it has very high internal resistance.

00:57 Who knows? they also tell us that when it is supplying current, that 20 watts of power are being supplied to an external load resistor of value r.

01:10 So we don't know the resistance.

01:13 And it asks us to find the resistance and find the internal resistance of the battery, the thing that's causing this sort of drop.

01:20 So to figure out part a, what is the resistance of the battery? we can use the information in this line right here.

01:34 I'll make that a little bit bigger.

01:36 This line right here, we can use this information to figure out the current flowing through the resistance.

01:45 If we know the current, we can then use oams law here to find the value of the resistance.

01:51 So the power equation, power is equal to current times voltage.

01:57 I know the voltage has been supplied to this resistance.

01:59 I also know the power caused by the battery through the resistor, so i can figure out what the current is.

02:12 So p is equal to i times v.

02:16 Solving this for i, we get current is equal to p divided by v, which is equal to 20 divided by 11 .6.

02:28 So, plugging that into our calculator, 20 divided by 11 .6, gives us a current flow of 1 .72 amps.

02:44 All right.

02:45 Now i'm going to take this current, drag it, and put it into here, and solve for r...

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