When a resistor with resistance R is connected to a 1.50 V flashlight battery, the resistor con

step 1 And this problem we're given the EMF and the battery is 1 .5 volts. It has a negligible internal

When a resistor with resistance R is connected to a 1.50 V...

When a resistor with resistance $R$ is connected to a $1.50 \mathrm{~V}$ flashlight battery, the resistor consumes $0.0625 \mathrm{~W}$ of electrical power. (Throughout, assume that each battery has negligible internal resistance.) (a) What power does the resistor consume if it is connected to a $12.6 \mathrm{~V}$ car battery? Assume that $R$ remains constant when the power consumption changes. (b) The resistor is connected to a battery and consumes $5.00 \mathrm{~W}$. What is the voltage of this battery?

Key Concepts

Ohm's Law

Ohm's Law establishes the fundamental relationship between voltage, current, and resistance in an electrical circuit through the equation V = IR. This principle is essential in analyzing circuits because it allows you to calculate any one of these three variables if the other two are known, providing a basis for understanding how changes to one will affect the others.

Power Dissipation in Resistors

Power dissipation in a resistor refers to the conversion of electrical energy into heat, quantified by equations such as P = I²R or P = V²/R. These formulas are pivotal in determining how much energy is used in a circuit component and predict outcomes when the applied voltage or resistance changes.

Voltage-Power Relationship

The voltage-power relationship in resistive circuits highlights that, for a fixed resistance, the power consumed is proportional to the square of the applied voltage. This quadratic dependence means that even small increases in voltage can result in significant increases in power consumption, which is crucial for safely designing and understanding electrical systems.

Transcript

00:01 And this problem we're given the emf and the battery is 1 .5 volts.

00:07 It has a negligible internal resistance.

00:12 And when a certain resistor, which is unknown, let's say as value r, is connected to this battery, it dissipates a power of 0 .0625 watts.

00:23 And in part a of the problem, we're asked, what power does the resistor consume if it is now connected to a 12 .6 volt car battery? so we can solve this problem by using equation 25 .18, which states that p is equal to the terminal voltage over the resistance squared.

00:58 I mean, over a terminal board is squared, over the resistance, not resistance squared, sorry.

01:06 And the first, so we need to make two steps in order to solve this problem.

01:15 So first, we'll find r, and once we find r, then we'll try to find the power that's dissipated by this resistor, given the new battery.

01:31 So right now we have information about the old battery and the power that's dissipated when this resistor is connected to the old battery.

01:41 So we have p and we have v.

01:45 We want to find r.

01:47 So r is v -a -p squared over p, which is since the internal resistance is negligible, it's exactly the emf of the battery, which is 1 .5 volt squared over 0 .0625 watts.

02:15 And this is 36 oms.

02:21 Okay, so now we have the resistance.

02:24 So using the very same equation, we want to find the power dissipated...

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