Question

1. During open-heart surgery, a defibrillator can be used to bring a patient out of cardiac arrest. The resistance of the path is 479.6 Ω and a 13.7 mA current is needed. What voltage should be applied?

2. A certain circuit breaker trips when the rms current is 16.8 A. What is the corresponding peak current?

3. A small office-building air conditioner operates on 402 V AC and consumes 48.9 kW. What is its effective resistance?

4. A power transmission line is hung from metal towers with glass insulators having a resistance of 1.18×10⁹ Ω . What current, in milliamps, flows through the insulator if the voltage is 173 kV? (Some high-voltage lines are DC, so don't let this trip you up.)

5. If the 0.107 mm diameter tungsten filament in a light bulb is to have a resistance of 0.184 Ω at 20.0 ºC , how long should it be in centimeters? (Tungsten has a resistivity of 5.6 x 10^-8 Ωm)

Answer 1

1.

Using Ohm's law:

V = I*R

V = 13.7*10^-3*479.6 = 6.57 V

2.

Relation between rms and peak current is given by:

I_Peak = Irms*sqrt (2)

I_peak = 16.8*sqrt (2) = 23.76 Amp

3.

Power consumed by electric device is given by:

P = V^2/R

R = Resistance = V^2/P = 402^2/(48.9*10^3)

R = 3.30 ohm

4.

Using Ohm's law:

V = I*R

I = V/R = 173*10^3/(1.18*10^9)

I = 0.146*10^-3 Amp = 0.146 milliamps

5.

Resistance of a wire is given by:

R = rho*L/A

L = R*A/rho = R*pi*d^2/(4*rho)

L = 0.184*pi*(0.107*10^-3)^2/(4*5.6*10^-8)

L = 0.0295 m = 2.95 cm

Let me know if you've any query.