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A3 DC Circuits

a1 Estimate the current through a wire if 2 C charge flows through a wire in 0.05 s?

a2 In an old style TV tube if the electron beam has 1 mA current, and if it takes 1 s to display one pixel (smallest bright spot), how much charge is deposited for each pixel?

a3 Look up quantitative information on lightning bolts, such as typical current, EMF, amount of charge transfer and duration of a single strike. List your values and the sources of information.

b1 Calculate the resistance of a Tungsten filament in light bulb at room temperature.
L = 10 cm, radius = 4 m. Use Ro = L/A .
Calculate the initial current through the filament as the light bulb is switched on, applying
potential difference V =120 Volt. Use Io = V/Ro .

In a fraction of second the filament heats up to 3000 oC above room temperature.
Calculate the new resistance, R, at the higher, operating, temperature.
Use: R = Ro[1 + (T-To)].

Calculate the steady state operating current. Use: I = V/R.

b2 Calculate R of a thin-film gold resistor:L = 1 m, width = 0.2 m, and thickness = 0.01 m.

c1.(a) Calculate the initial power in the light bulb discussed above (see b1), using c.

(b) Calculate the steady state power when the filament is hot, using c.

(c ) Using your answers to (a) and (b) above, explain why light bulb tend to burn out
just when they are switched on.

c2. The 120 V 'line voltage' is actually Vrms . What is the voltage amplitude, Vo ?
Use c.

c3. A Battery is rated as 20 volt.amp.hour. Calculate the energy stored in it.
Use: E = P*t (Recall from Physics I, Watt = Joule/sec, so Joule = Watt*Sec)

d1 Take: R1 = 100  , R2 = 300 , R3 = 200  and R4 = 1000 

(a) Calculate the series combination of R1 and R2 .
(b) Calculate the parallel combination of R1 and R4.
(c) Calculate the total resistance of the circuit shown. Use the PROCEDURE.

d2 R1 = 100  , R2 = 300 , R3 = 200 
In the circuit diagram below, the total current flowing through the circuit is 1 Amp, calculate the total power using P = I2*Rtotal , and then verify the answer by calculating power dissipated in each of the resistors and doing the sum.
e1. Consider the following circuit, where Eo= 12 volt, and r = 5 .

(a) Calculate the current supplied by the battery.
(b) Calculate the terminal voltage, V.
(c) Calculate the power dissipated within the battery (Pb = E * I)

e2. Redo the above exercise with a new internal resistance of 20  instead of original 5 .

f1. Application of Kirchhoff's Laws

(a) Use KCL at point C: I=0
I1 -I2 -I3 = 0

(b) KVL applied to loop ABCFA: V=0
V1 -I1R1 -I2R2 = 0

(c) KVL applied to loop EFCDE: V=0
+I2R2 -I3R3 + V2 = 0

(d) Solve for current through each resistors

(e) Solve for power dissipated in each resistor (use I2R for each), and show that the total equal to the power supplied by the two sources (V1I1+V2I3).

g1. Three 120 V outlets are connected in parallel through a 20 A circuit breaker, to a single 120 V source. Is the breaker going to trip, if a 1500 W toaster, 1100 W iron and a 1000 W microwave are plugged into aforementioned outlets, and being used at the top power rating?

g2. Given 2000 V potential difference, what ought to be the resistance between two point of body, for fatal amount of current to flow through heart region? How does it compare with the measured resistance between your index fingers?

h1. (a) Calculate capacitance for a parallel plate capacitor, where A = 0.25 cm2, d = 0.5 cm.
Use Co = oA/d.
(b) Calculate the new value of the capacitance if the gap is filled by rubber.
Use C = Co.
(c) If the applied voltage between the plates is 2 volt, what is the charge on each plate?

h2 (a) Calculate the energy stored in mica filled capacitor if
A = 1 m2, d = 0.01m, V = 10,000 volts.
(b) Calculate the energy density, in the above.

h3 Take: C1 = 100 F, C2 = 300 F, C3 = 200 F
(a) Calculate the total capacitance of the circuit shown.

(b) If in the total voltage across the circuit is 10 V, calculate the charge on each capacitor and the total energy stored. (Recall: U = 0.5CV2)

i4 Charging Capacitor
For R = 1000 , C = 4000 F, Vo= 12 volt.
(a) Calculate time when Q = Qmax/2.
(b) Calculate time when I = 0.25Io.

j5 Discharging Capacitor
For R = 1000 , C = 2000 F, Qo= 20 mC.
(a) How long will it take before the capacitor discharges to Qo/100.
(b) What is the value of current at t = 4 sec.

https://brainmass.com/physics/power/electric-circuits-charging-capacitor-414083

#### Solution Preview

a1) Estimate the current through a wire if 2 μC charge flows through a wire in 0.05 s?

Solution:
Current=Charge/Time=2μC/(0.05 s)=(2×〖10〗^(-6) C)/(0.05 s)=4×〖10〗^(-5) Ampere

a2) In an old style TV tube if the electron beam has 1 mA current, and if it takes 1 μs to display one pixel (smallest bright spot), how much charge is deposited for each pixel?

Solution:

Current=Charge/Time

Or,Charge=Current×Time
=1mA×1μs
=1×〖10〗^(-3) A×1×〖10〗^(-6) s
=1×〖10〗^(-9) Coulomb

A charge of 1×〖10〗^(-9) Coulomb is deposited on each pixel.

b1) Calculate the resistance of a Tungsten filament in light bulb at room temperature.
L = 10 cm, radius = 4 μm. Use Ro = ρ L/A.

Solution:
Resistance,Ro = ρ L/A=(5.6×〖10〗^(-8) Ohm.m)×(10×〖10〗^(-2) m)/(π(4×〖10〗^(-6) )^2 m^2 )=111.408 Ohm

Calculate the initial current through the filament as the light bulb is switched on, applying
Potential difference V =120 Volt. Use Io = V/Ro

Solution:

Io =V/Ro=(120 Volt)/(111.408 Ohm)=1.077 Ampere

In a fraction of second the filament heats up to 3000 oC above room temperature.
Calculate the new resistance, R, at the higher, operating, temperature.
Use: R = Ro [1 + α (T-To)].
Solution:

Resistance,R = Ro [1 + α (T-To)]
=111.408 Ohm [1+0.0045(3000-20)]
=1605.389 Ohm

Calculate the steady state operating current. Use: I = V/R

Solution:

Steady State Operating Current,I =V/R=120Volt/(1605.389 Ohm)=0.0747 Ampere

b2) Calculate R of a thin-film gold resistor: L = 1 μm, width = 0.2 μm, and thickness = 0.01 μm.

Solution:

Resistance,R = ρ L/A=(2.44×〖10〗^(-8) Ohm.m)×(1×〖10〗^(-6) m)/(0.2×〖10〗^(-6) m×0.01×〖10〗^(-6) m)=12.2 Ohm

c1) (a) Calculate the initial power in the light bulb discussed above (see b1), using c.

Solution:
Initial Power,P=V^2/R_0 =(120V)^2/(111.408 Ohm)=129.255 Watt

(b) Calculate the steady state power when the filament is hot, using c .

Solution:
Steady State Power,P=V^2/R_0 =(120V)^2/(1605.389 Ohm)=8.970 Watt

(c) Using your answers to (a) and (b) above, explain why light bulbs tend to burn out just when they are switched on.

Solution:

Initially, the resistance is low and hence the current flowing through the bulb filament is high. Within a fraction of a sec, the resistance increases and the current through the filament decreases. The initial power in the light bulb is also very high as compared to the steady state power. Hence, light bulbs tend to burn out just when they are switched on.

c2) The 120 V 'line voltage' is actually Vrms . What is the voltage amplitude, Vo?
Use c .

Solution:

V_RMS=120V

V_0=√2×V_RMS=√2×120V=169.706 V

c3) A Battery is rated as 20 volt.amp.hour. Calculate the energy stored in it.
...

#### Solution Summary

Electric circuits and charging capacitors for AC currents are determined. The current through a wire is estimated.

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