(a) How much charge does a battery have to supply to a 5.0μF capacitor to create a potential dif

(a) How much charge does a battery have to supply to a 5.0μF...

(a) How much charge does a battery have to supply to a 5.0$\mu \mathrm{F}$ capacitor to create a potential difference of 1.5 $\mathrm{V}$ across its plates? How much energy is stored in the capacitor in this case? (b) How much charge would the battery have to supply to store 1.0 $\mathrm{J}$ of energy in the capacitor? What would be the potential across the capacitor in that case?

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Key Concepts

Capacitance

Capacitance is a measure of a capacitor's ability to store charge per unit voltage. It is defined by the relation C = Q/V, where C is the capacitance, Q is the charge stored, and V is the potential difference across the capacitor's plates. This concept is fundamental in understanding how capacitors work in circuits and energy storage systems.

Relationship between Charge and Voltage

The relationship between charge and voltage in a capacitor is given by the equation Q = CV. This linear relationship indicates that the amount of stored charge is directly proportional to both the capacitance and the applied voltage. It is a key concept in both circuit analysis and in solving practical problems involving capacitors.

Energy Stored in a Capacitor

The energy stored in a capacitor is due to the electric field established between its plates when charged. The energy can be calculated using the formula U = 1/2 CV² or, equivalently, U = Q²/(2C). This concept is crucial for applications where energy storage and discharge are important, such as in power supply filters and energy storage devices.

Transcript

00:01 So in this question, we're wondering about the charge that a battery would supply if we had a 5 micro -faird capacitor and then we had 1 .5 volts.

00:12 So voltage is 1 .5 volts.

00:17 And the capacitance is 5 micro -farad.

00:28 Q is cv.

00:31 So we just multiply those.

00:33 Oh i can do that one in my head.

00:36 That's just 7 .5 microculum.

00:46 And then we want to get the energy stored.

00:50 And so u is equal to 1 .5.

00:55 C .v.

00:57 Squared.

00:58 So it's just going to be 1 .5 times 5 times 10 to the minus 6 times 1 .5 squared.

01:10 So let's go ahead and plug that into a calculator times 5 times 10 to the minus 6.

01:25 So that's 5 .6 microjoules.

01:42 And so let me go ahead and label these.

01:45 So this is a, this is b.

01:49 Now to approach c, oh, i guess that was both a.

01:55 Those were both a how much charge we're wondering how much charge if we wanted to add one jewel of energy to the capacitor and so for that let's use um let's see sorry so how much charge so we're looking for q we have the and we have c and we have um and we have you so q, c, and u.

02:40 So let's use u is one half q squared over c...

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