Flashcards: Capacitors, Limits, and Reproduction — 67 cards

How is charge related to current and time for a capacitor charged by constant current?

Charge equals current multiplied by time, $q=It$.

What is the voltage across a capacitor charged by constant current with zero initial voltage?

Voltage is $u_C(t)=\frac{I}{C}t$.

What is the voltage across a resistor carrying a constant current?

Voltage equals resistance times current, $u_R=RI$.

What is the current in the given circuit?

The current is $8\,\mathrm{mA}$.

What is the capacitance in the given circuit?

The capacitance is $5\times10^{-3}\,\mathrm{F}$.

After how long does the capacitor reach 20 V in the given circuit?

The capacitor reaches 20 V after $12.5\,\mathrm{s}$.

What does an ideal current generator deliver?

A constant current intensity.

What remains constant in an ideal current generator's ammeter reading?

The current intensity.

What does an ideal voltage generator maintain constant between terminals P and N?

The potential difference.

What is the formula for the potential difference in an ideal voltage generator?

$u_{PN}=E=\mathrm{constant}$.

How is a real cell modeled in terms of voltage and current?

By the formula $u_{PN}=E-rI$.

In the formula $u_{PN}=E-rI$, what does E represent?

The electromotive force of the cell.

In the formula $u_{PN}=E-rI$, what does the term $rI$ represent?

The internal voltage drop.

What differential equation does the charge satisfy in a charging circuit with resistances R and R1?

$\frac{dq}{dt}+\frac{q}{(R+R_1)C}=\frac{E}{R+R_1}$

What is the formula for the time constant $\tau$ in the RC charging circuit?

$\tau=(R+R_1)C$

How is the forcing constant $h$ defined in the charging circuit?

$h=\frac{E}{R+R_1}$

What is the charge $q(t)$ for an initially uncharged capacitor?

$q(t)=\tau h\left(1-e^{-t/\tau}\right)$

What is the voltage across resistor $R_1$ during charging?

$u_{R1}(t)=R_1h e^{-t/\tau}$

What is the charging duration when the capacitor reaches 99.9% charge?

Approximately $\Delta t=7\tau=7(R+R_1)C$.

What is the capacitance value from the experimental straight line?

$C=20\,\mu\mathrm{F}$.

What is the fixed resistance value from the experimental data?

$R_1=100\,\Omega$.

What time constant $\tau$ does the tangent method give?

$\tau=5\,\mathrm{ms}$.

What is the adjustable resistance $R_0$ calculated from $\tau$?

$R_0=150\,\Omega$.

What is the initial resistor current $h$ used in the calculation?

$h=4\times10^{-2}\,\mathrm{A}$.

What is the source emf $E$ determined from the initial resistor voltage?

$E=10\,\mathrm{V}$.

What is the formula for electric energy stored in a capacitor?

$E_e=\frac{q^2}{2C}=\frac12Cu_C^2$

What is the formula for stored energy with constant current charging an uncharged capacitor?

$E_e=\frac{I^2}{2C}t^2$

What is the capacitance formula for a parallel-plate capacitor?

$C=\varepsilon\frac{S}{e}$

How is relative permittivity defined in terms of permittivity?

$\varepsilon_r=\frac{\varepsilon}{\varepsilon_0}$

What happens to capacitor charge during constant-current charging?

The capacitor charge increases.

How does the voltage of a capacitor change during constant-current charging?

The voltage rises linearly.

How does stored energy change during constant-current charging of a capacitor?

Stored energy increases quadratically.

What equation relates charge and current in a capacitor charged by constant current?

$q=It$

What charges do the two plates of a capacitor carry when charged?

One plate carries +q and the other carries −q.

What is the formula for capacitance with a dielectric in this course?

$C=\varepsilon\frac{S}{e}$

In the capacitor formula $C=\varepsilon\frac{S}{e}$, what does S represent?

S is the plate area.

In the capacitor formula $C=\varepsilon\frac{S}{e}$, what does e represent?

e is the dielectric thickness.

What are the steps to solve a limit problem?

Establish a bound or equivalent expression, determine the limit, interpret the result.

When does the squeeze theorem apply?

When a function is bounded between two functions with the same limit.

What defines continuity of a function at a point?

Its limit at that point exists and equals the function value there.

How is continuity checked at a joining point of a piecewise function?

By comparing left-hand limit, right-hand limit, and function value.

What does a finite limit at infinity indicate about a function?

It identifies a horizontal asymptote.

What can a divergent quotient like f(x)/x reveal about a function?

It identifies a branch direction.

Which property ensures existence of a solution on an interval?

Continuity of the function.

Which property guarantees uniqueness of a solution to an equation?

Strict monotonicity of the function.

What does the identity $1+e^{i\theta}$ convert into?

It converts into $2\cos\left(\frac\theta2\right)e^{i\theta/2}$.

What does a real value of $\frac{z_M-z_B}{z_M-z_A}$ imply about vectors MA and MB?

Vectors MA and MB are collinear in direction.

What geometric property does triangle ABM have when $\frac{z_M-z_B}{z_M-z_A}=\frac1{\sqrt6}$ is real?

Triangle ABM is right-angled at M.

What shape is OACD according to the course?

OACD is a rhombus.

What is the area of rhombus OACD?

Its area is $6\sin\theta$.

Where is Gonadoliberin secreted from?

The hypothalamus.

What sequence does male reproductive regulation follow?

Hypothalamus secretes GnRH, pituitary secretes gonadostimulins, testis produces testosterone and supports spermatogenesis.

What effect does testosterone have on the hypothalamo-pituitary complex?

It exerts negative feedback to regulate gonadostimulin secretion.

Is a vesicle seminalis an endocrine or exocrine gland?

It is an accessory exocrine gland.

What does a vesicle seminalis contribute to semen?

It contributes seminal fluid.

What is spermiogenesis in male gametogenesis?

The differentiation of spermatids into spermatozoa.

Where does spermiogenesis occur in the male reproductive system?

In the seminiferous tubule, not in the epididymis.

How does spermatogenesis differ from oogenesis in cytoplasmic division?

Spermatogenesis has equal cytoplasmic divisions, oogenesis has unequal.

Is spermatogenesis continuous or discontinuous?

Spermatogenesis is continuous.

What is the corpus luteum?

A temporary structure formed from a follicle after ovulation.

What effect does castration have on gonadostimulin secretion in pubescent animals?

It causes gonadostimulin hypersecretion.

Why do accessory glands atrophy after castration in pubescent animals?

Because testicular negative feedback is removed.

What changes occur in S2 after GnRH injection in the experiment?

LH rises from 0.51 to 9 and testosterone from 6 to 16.

How does S3 respond to GnRH injection in terms of LH and testosterone?

LH remains about 0.6 and testosterone about 6.9, unchanged.

What does a response to discontinuous GnRH injection indicate about hypothalamic and pituitary-testis function?

The hypothalamic signal is deficient but the pituitary-testis pathway can respond.

What are the normal reference ranges for LH and testosterone?

LH is 1–9 mU/L and testosterone is 10–30 nmol/L.

What steps are involved in experimentally diagnosing infertility?

Compare germ-cell DNA content and numbers, test GnRH response, and localize defect from hormones.