Key cards

What is capacitance defined as?

Capacitance (C) is defined as C = Q / V, where Q is the charge and V is the voltage.

How is capacitance calculated for a parallel plate capacitor with no dielectric?

Capacitance (C) for a parallel plate capacitor with no dielectric is calculated as C = εo A / d, where εo is the permittivity of free space, A is the area, and d is the separation.

What effect does a dielectric have on the capacitance of a capacitor?

A dielectric increases the capacitance of a vacuum-spaced capacitor.

In a parallel plate capacitor, if the E field is uniform what is E= ?

In a uniform electric field (E) within a parallel plate capacitor, E = V / d, where V is the voltage and d is the separation.

How is the energy stored in a capacitor calculated?

The energy (U) stored in a capacitor is given by the equation U = \frac{1}{2}QV, where Q is the charge and V is the voltage.

What are the equations for capacitors in series and parallel?

Capacitors in series: \frac{1}{C{total}} = \frac{1}{C1} + \frac{1}{C2} + … Capacitors in parallel: C{total} = C1 + C2 + …

What are the equations for the charging and discharging of a capacitor through a resistor?

Charging: Q = Qo (1 - e^{-t / RC}) Discharging: Q = Qo e^{-t / RC}, where RC is the time constant.

How is gravitational field strength calculated for spherical bodies?

The gravitational field outside spherical bodies is calculated as if the whole mass were concentrated at the center.

What do equipotential surfaces indicate?

Equipotential surfaces join points of equal potential and are spherical for a point charge.

What equation is used for gravitational potential energy change over negligible height variations?

The equation \Delta U_P = mg\Delta h is used for distances over which the variation of g is negligible.

State Newton's law of gravitation.

Newton's law of gravitation: F = G \frac{M1 M2}{r^2}, where G is the gravitational constant, M1 and M2 are the masses, and r is the distance between them.

How can Kepler's 3rd law be derived from Newton's law of gravity?

Kepler's 3rd law (for circular orbits) is derived from Newton's law of gravity and the formula for centripetal acceleration.

How can data on orbital motion be used to calculate the mass of the central object?

Data on orbital motion (period or orbital speed) can be used to calculate the mass of the central object using gravitational relationships.

What does the Doppler relationship state?

The Doppler relationship is expressed as \frac{\Delta \lambda}{\lambda} = \frac{v}{c}, where Δλ is the change in wavelength, λ is the original wavelength, v is the velocity, and c is the speed of light.

How is Hubble's constant defined?

Hubble's constant (H0) relates galactic radial velocity (v) to distance (D) and is defined by v = H0D.

Why does 1 / H_0 approximate the age of the universe?

Because it represents the time taken for galaxies to reach their current separation if they have been moving at a constant speed since the beginning of the universe.

What is magnetic flux defined as?

Magnetic flux (Φ) is defined as Φ = AB cos Θ, and flux linkage = NΦ, where A is the area, B is the magnetic field, and Θ is the angle.

State Faraday's and Lenz's laws.

Faraday's Law: The induced emf is equal to the rate of change of magnetic flux linkage. Lenz's Law: The direction of the induced emf opposes the change producing it.

How is the attenuation of X-rays calculated?

The attenuation of X-rays is given by the equation I = I0 exp(-\mu x), where I is the intensity, I0 is the initial intensity, μ is the attenuation coefficient, and x is the thickness.

What is acoustic impedance defined as?

Acoustic impedance (Z) is defined by Z = pc, where p is the density and c is the speed of sound.

How is the Doppler equation used to study blood flow?

The Doppler equation \frac{\Delta f}{f0} = \frac{2v}{c} is used to study blood flow, where Δf is the change in frequency, f0 is the original frequency, v is the velocity of blood flow, and c is the speed of sound.

How is the Lamor frequency calculated in MRI?

The Lamor frequency (f) is calculated by f = 42.6 \times 10^6 B, where B is the magnetic field.

Define the Gray (Gy) and Sievert (Sv).

Gray (Gy): unit of absorbed dose, defined as energy per kilogram. Sievert (Sv): unit of equivalent dose and effective dose.

How are equivalent dose and effective dose calculated?

Equivalent dose (H) = Absorbed dose (D) × Radiation weighting factor (WR) = DWR. Effective dose (E) = Equivalent dose (H) × Tissue weighting factor (WT) = HWT.

Formulas and Quantities Covered

Here is a quick recap: C=Q/V, C = εo A / d, E = V / d, U = \frac{1}{2}QV, Series: \frac{1}{C{total}} = \frac{1}{C1} + \frac{1}{C2} + …, Parallel: C{total} = C1 + C2 + …, Charging: Q = Qo (1 - e^{-t / RC}), Discharging: Q = Qo e^{-t / RC}, \Delta UP = mg\Delta h, F = G \frac{M1 M2}{r^2}, $$\frac{\Delta \lambda}{\lambda} = \frac{v}{c}$