A Twelve Picofarad Capacitor

Q. A 12 pF capacitor is connected to a 50 V battery. How much electrostatic energy is stored in the capacitor, in joules? expects 1.5 × 10⁻⁸ J

What the draft establishes

Fills in once a draft is checked.

The web of concepts

given read from the words equation asked

The equations it used

None yet.

Check an answer

Q. A 12 pF $C = 12$ pF capacitor is connected to a 50 V $V = 50$ V battery. How much electrostatic energy is stored in the capacitor, in joules?

The playground

Inputs

capacitance

C

12 pF

battery

V

50 V

Outputs

energy

U

The solution

Solved with Capacitance

Given

$C = 12$ pF
$V = 50$ V

Find $U$ .

Working

$C = 12$ pF $= 1.2 \times 10^{−11}$ F
energy in a capacitor(capacitor) $U = \frac{C \cdot V^{2}}{2}$
$U = \frac{1.2 \times 10^{−11} \cdot 50^{2}}{2}$
$U = 1.5 \times 10^{−8}$ J
$U \approx 1.5 \times 10^{−8}$ Jto 2 significant figures

Conclusion

Charging a capacitor takes work against the charge already on it, and that work is stored as half the capacitance times the square of the voltage.

The Ruby

1require_relative "../physics"23question :a_twelve_picofarad_capacitor do4  kind :numerical5  describes "A %{capacitance} capacitor is connected to a %{battery} battery. %{energy}, in joules?"6  given capacitance: "12 pF"7  given battery: "50 V"8  asks energy: "How much electrostatic energy is stored in the capacitor"9end

1require_relative "../questions/a_twelve_picofarad_capacitor"2require_relative "../science/electrostatic_potential_and_capacitance/capacitance"34solve :a_twelve_picofarad_capacitor, using: Capacitance do5  objects :capacitor67  take capacitance: capacitor.capacitance8  take battery: capacitor.voltage910  energy = capacitor.energy_stored11  answer energy:, in: "J", figures: 21213  conclusion "Charging a capacitor takes work against the charge already on it, and that work is stored as " \14             "half the capacitance times the square of the voltage."15end

1require_relative "../solutions/a_twelve_picofarad_capacitor"23play_with :a_twelve_picofarad_capacitor do4  title "A Twelve Picofarad Capacitor"5end

The laws

quantity	written	units	within	from
permittivity of free space	$ε_{0}$	F/m	—	Capacitance
capacitance	$C$	F	0 … ∞	Capacitance
charge	$Q$	C	—	Capacitance
voltage	$V$	V	—	Capacitance
energy stored	$U$	J	—	Capacitance
area	$A$	m²	—	Capacitance
plate separation	$d$	m	—	Capacitance
dielectric constant	$K$	—	—	Capacitance
charge of ground	$Q_{g}$	C	—
capacitance of ground	$C_{g}$	F	0 … ∞
voltage of ground	$V_{g}$	V	—
charge of capacitor	$Q$	C	—
capacitance of capacitor	$C$	F	0 … ∞
voltage of capacitor	$V$	V	—
dielectric constant of ground	$K_{g}$	—	—
area of ground	$A_{g}$	m²	—
plate separation of ground	$d_{g}$	m	—
dielectric constant of capacitor	$K$	—	—
area of capacitor	$A$	m²	—
plate separation of capacitor	$d$	m	—
energy stored of ground	$U_{g}$	J	—
energy stored of capacitor	$U$	J	—

Q_{c} = C_{c} \cdot V_{c}

charge on a capacitor

C_{c} = \frac{K_{c} \cdot ε_{0} \cdot A_{c}}{d_{c}}

a parallel plate capacitor

U_{c} = \frac{C_{c} \cdot {V_{c}}^{2}}{2}

energy in a capacitor

Q_{g} = C_{g} \cdot V_{g}

charge on a capacitor(ground)

Q = C \cdot V

charge on a capacitor(capacitor)

C_{g} = \frac{K_{g} \cdot ε_{0} \cdot A_{g}}{d_{g}}

a parallel plate capacitor(ground)

C = \frac{K \cdot ε_{0} \cdot A}{d}

a parallel plate capacitor(capacitor)

U_{g} = \frac{C_{g} \cdot {V_{g}}^{2}}{2}

energy in a capacitor(ground)

U = \frac{C \cdot V^{2}}{2}

energy in a capacitor(capacitor)