Physics, 31.03.2020 04:24 alexabessin

Establishing a potential difference The deflection plates in an oscilloscope are 10 cm by 2 cm with a gap distance of 1 mm. A 100 volt potential difference is suddenly applied to the initially uncharged plates through a 975 ohm resistor in series with the deflection plates. How long does it take for the potential difference between the deflection plates to reach 75 volts

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Answer from: lia3865

t = 23.9nS

Explanation:

given :

Area A= 10 cm by 2 cm => 2 x 10^-2m x 10 x 10^-2m

distance d= 1mm=> 0.001

resistor R= 975 ohm

Capacitance can be calculated through the following formula,

C = (ε0 x A )/d

C = (8.85 x 10^-12 x (2 x 10^-2 x 10 x 10^-2))/0.001

C = 17.7 x 10^-12 (pico 'p' = 10^-12)

C = 17.7pF

the voltage between two plates is related to time, There we use the following formula of the final voltage

Vc = Vx (1-e^-(t/CR))

75 = 100 x (1-e^-(t/CR))

75/100 = (1-e^-(t/CR))

.75 = (1-e^-(t/CR))

.75 -1 = -e^-(t/CR)

-0.25 = -e^-(t/CR) --->(cancelling out the negative sign)

e^-(t/CR) = 0.25

in order to remove the exponent, take logs on both sides

-t/CR = ln (0.25)

t/CR = -ln(0.25)

t = -CR x ln (0.25)

t = -(17.7 x 10^-12 x 975) x (-1.38629)

t = 23.9 x $10^{-9$

t = 23.9ns

Thus, it took 23.9ns for the potential difference between the deflection plates to reach 75 volts

Answer from: davelopez979

t = 24.3ns

Explanation:

The deflection plates make up a parallel plate capacitor fed via 975 ohm resistor from a 100V supply

capacitance C = (e0 x A) / d

C = $\frac{(8.85 X 10^{-12} X (2 X 10^{-2} X 10 X 10^{-2} ) )}{10^{-3} }$

C = $C = 18 X 10^{-12} F$

$Vc = Vx (1-e^{-(\frac{t}{CR} )} )$

$75 = 100 X (1-e^{-(\frac{t}{CR} )} )$

$\frac{75}{100} = (1-e^-{(\frac{t}{CR} )} )$

$0.75 = (1-e^{-(\frac{t}{CR} )} )$

$0.75 - 1 = -e^{-(\frac{t}{CR} )}$

$e^{-(\frac{t}{CR} )} = 0.25$

Taking the logs of both sides

$-(\frac{t}{CR} ) = In(0.25)$

$(\frac{t}{CR} ) = -In(0.25)$

t = =CR x In (0.25)

$t = (18 X 10^{-12} X 975) X (-1.386)$

t = 2.43 x 10∧-9

t = 24.3ns

Answer from: Quest

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Answer from: Quest

Ohm's law tells you that i = v/r where v is equivalent voltage and r is equivalent resistance of the circuit
since all circuits have the same voltage, your question is really asking which circuit has the lowest total resistance, since the lower the resistance, the higher the current
circuit a has a resistance of 5 ohms; circuit c is in series so has a resistance of 10 ohms; circuit b is in parallel and therefore has a resistance of 2.5 ohms (review your notes on adding resistances in parallel and series); therefore b has the highest current

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Establishing a potential difference The deflection plates in an oscilloscope are 10 cm by 2 cm with...

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