When a 360 -nF air capacitor (1 nF=10^-9 F) is connected to a power supply, the energy stored in

step 1 Everybody. So this one, we need to find what is a potential difference between the capture plate

When a 360 -nF air capacitor (1 nF=10^-9 F) is connected to...

When a 360 -nF air capacitor $\left(1 \mathrm{nF}=10^{-9} \mathrm{F}\right)$ is connected to a power supply, the energy stored in the capacitor is $1.85 \times 10^{-5} \mathrm{J}$ . While the capacitor is kept connected to the power supply, a slab of dielectric is inserted that completely fills the space between the plates. This increases the stored energy by $2.32 \times 10^{-5} \mathrm{J}$ . (a) What is the potential difference between the capacitor plates? (b) What is the dielectric constant of the slab?

When a 360 -nF air capacitor $\left(1 \mathrm{nF}=10^{-9} \mathrm{F}\right)$ is connected to a power supply, the energy stored in the capacitor is $1.85 \times 10^{-5} \mathrm{J}$ . While the capacitor is kept connected to the power supply, a slab of dielectric is inserted that completely fills the space
between the plates. This increases the stored energy by $2.32 \times 10^{-5} \mathrm{J}$ . (a) What is the potential difference between the capacitor plates? (b) What is the dielectric constant of the slab?

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Key Concepts

Capacitor Energy Storage

Capacitors store energy in the electric field between their plates, and the energy is given by the formula U = (1/2)CV², where C is the capacitance and V is the voltage across the plates. This relationship is fundamental in understanding how changes in voltage or capacitance directly affect the energy stored in a capacitor.

Dielectric Materials in Capacitors

Dielectric materials, when inserted between the plates of a capacitor, increase the capacitance by a factor equal to the dielectric constant (????). The presence of a dielectric reduces the effective electric field, allowing more charge to be stored at the same applied voltage. This effect is crucial in applications where enhancing a capacitor’s storage capacity is desired.

Constant Voltage Conditions

When a capacitor is connected to a power supply, the voltage across its plates is maintained constant. Under these conditions, any change in capacitance—such as that caused by the insertion of a dielectric—leads to a change in the stored energy while the voltage remains fixed. Understanding this constant voltage scenario is essential for correctly analyzing and predicting the behavior of the system when modifications, like dielectric insertion, are made.

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