# 10.6 Household wiring and electrical safety  (Page 4/11)

 Page 4 / 11

## Summary

• The two types of electric hazards are thermal (excessive power) and shock (current through a person). Electrical safety systems and devices are employed to prevent thermal and shock hazards.
• Shock severity is determined by current, path, duration, and ac frequency.
• Circuit breakers and fuses interrupt excessive currents to prevent thermal hazards.
• The three-wire system guards against thermal and shock hazards, utilizing live/hot, neutral, and ground wires, and grounding the neutral wire and case of the appliance.
• A ground fault circuit interrupter (GFCI) prevents shock by detecting the loss of current to unintentional paths.

## Key equations

 Terminal voltage of a single voltage source ${V}_{\text{terminal}}=\epsilon -I{r}_{\text{eq}}$ Equivalent resistance of a series circuit ${R}_{\text{eq}}={R}_{1}+{R}_{2}+{R}_{3}+\text{⋯}+{R}_{N-1}+{R}_{N}=\sum _{i=1}^{N}{R}_{i}$ Equivalent resistance of a parallel circuit ${R}_{\text{eq}}={\left(\frac{1}{{R}_{1}}+\frac{1}{R2}+\text{⋯}+\frac{1}{{R}_{N}}\right)}^{-1}={\left(\sum _{i=1}^{N}\frac{1}{{R}_{i}}\right)}^{-1}$ Junction rule $\sum {I}_{\text{in}}=\sum {I}_{\text{out}}$ Loop rule $\sum V=0$ Terminal voltage of N voltage sources in series ${V}_{\text{terminal}}=\sum _{i=1}^{N}{\epsilon }_{i}-I\sum _{i=1}^{N}{r}_{i}=\sum _{i=1}^{N}{\epsilon }_{i}-I{r}_{\text{eq}}$ Terminal voltage of N voltage sources in parallel ${V}_{\text{terminal}}=\epsilon -I{\sum _{i=1}^{N}\left(\frac{1}{{r}_{i}}\right)}^{-1}=\epsilon -I{r}_{\text{eq}}$ Charge on a charging capacitor $q\left(t\right)=C\epsilon \left(1-{e}^{-\frac{t}{RC}}\right)=Q\left(1-{e}^{-\frac{t}{\tau }}\right)$ Time constant $\tau =RC$ Current during charging of a capacitor $I=\frac{\epsilon }{R}{e}^{-\frac{t}{RC}}={I}_{o}{e}^{-\frac{t}{RC}}$ Charge on a discharging capacitor $q\left(t\right)=Q{e}^{-\frac{t}{\tau }}$ Current during discharging of a capacitor $I\left(t\right)=-\frac{Q}{RC}{e}^{-\frac{t}{\tau }}$

## Conceptual questions

Why isn’t a short circuit necessarily a shock hazard?

We are often advised to not flick electric switches with wet hands, dry your hand first. We are also advised to never throw water on an electric fire. Why?

Not only might water drip into the switch and cause a shock, but also the resistance of your body is lower when you are wet.

## Problems

(a) How much power is dissipated in a short circuit of 240-V ac through a resistance of $0.250\phantom{\rule{0.2em}{0ex}}\text{Ω}$ ? (b) What current flows?

What voltage is involved in a 1.44-kW short circuit through a $0.100\text{-}\text{Ω}$ resistance?

12.0 V

Find the current through a person and identify the likely effect on her if she touches a 120-V ac source: (a) if she is standing on a rubber mat and offers a total resistance of $300\phantom{\rule{0.2em}{0ex}}\text{k}\text{Ω}$ ; (b) if she is standing barefoot on wet grass and has a resistance of only $4000\phantom{\rule{0.2em}{0ex}}\text{k}\text{Ω}$ .

While taking a bath, a person touches the metal case of a radio. The path through the person to the drainpipe and ground has a resistance of $4000\phantom{\rule{0.2em}{0ex}}\text{Ω}$ . What is the smallest voltage on the case of the radio that could cause ventricular fibrillation?

400 V

A man foolishly tries to fish a burning piece of bread from a toaster with a metal butter knife and comes into contact with 120-V ac. He does not even feel it since, luckily, he is wearing rubber-soled shoes. What is the minimum resistance of the path the current follows through the person?

(a) During surgery, a current as small as $20.0\phantom{\rule{0.2em}{0ex}}\mu \text{A}$ applied directly to the heart may cause ventricular fibrillation. If the resistance of the exposed heart is $300\phantom{\rule{0.2em}{0ex}}\text{Ω},$ what is the smallest voltage that poses this danger? (b) Does your answer imply that special electrical safety precautions are needed?

a. 6.00 mV; b. It would not be necessary to take extra precautions regarding the power coming from the wall. However, it is possible to generate voltages of approximately this value from static charge built up on gloves, for instance, so some precautions are necessary.

what is flux
Total number of field lines crossing the surface area
Kamru
Basically flux in general is amount of anything...In Electricity and Magnetism it is the total no..of electric field lines or Magnetic field lines passing normally through the suface
prince
what is temperature change
Celine
a bottle of soft drink was removed from refrigerator and after some time, it was observed that its temperature has increased by 15 degree Celsius, what is the temperature change in degree Fahrenheit and degree Celsius
Celine
process whereby the degree of hotness of a body (or medium) changes
Salim
Q=mcΔT
Salim
where The letter "Q" is the heat transferred in an exchange in calories, "m" is the mass of the substance being heated in grams, "c" is its specific heat capacity and the static value, and "ΔT" is its change in temperature in degrees Celsius to reflect the change in temperature.
Salim
what was the temperature of the soft drink when it was removed ?
Salim
15 degree Celsius
Celine
15 degree
Celine
ok I think is just conversion
Salim
15 degree Celsius to Fahrenheit
Salim
0 degree Celsius = 32 Fahrenheit
Salim
15 degree Celsius = (15×1.8)+32 =59 Fahrenheit
Salim
I dont understand
Celine
the question said you should convert 15 degree Celsius to Fahrenheit
Salim
To convert temperatures in degrees Celsius to Fahrenheit, multiply by 1.8 (or 9/5) and add 32.
Salim
what is d final ans for Fahrenheit and Celsius
Celine
it said what is temperature change in Fahrenheit and Celsius
Celine
the 15 is already in Celsius
Salim
So the final answer for Fahrenheit is 59
Salim
what is d final ans for Fahrenheit and Celsius
Celine
what are the effects of placing a dielectric between the plates of a capacitor
increase the capacitance.
Jorge
besides increasing the capacitance, is there any?
Bundi
mechanical stiffness and small size
Jorge
why for an ideal gas internal energy is directly proportional to thermodynamics temperature?
two charged particles are 8.45cm apart. They are moved and the force on each of them is found to have tripled. How far are they now?
what is flux
Bundi
determining dimensional correctness
determine dimensional correctness of,T=2π√L/g
PATRICK
somebody help me answer the question above
PATRICK
calculate the heat flow per square meter through a mineral roll insulation 5cm thick if the temperature on the two surfaces are 30degree Celsius and 20 degree Celsius respectively. thermal conduction of mineral roll is 0.04
what are the elementary compositions of a cell?
poles, chemical
prabir
when a current pass through a material does the velocity varies
no.
prabir
what is spin entropy ?and disorder in ferromagnetic material
diagram of an hall effect sensor
if a magnetised wire having dipole moment M is bent in the form of arc subtending angle of 45°at centre,new magnetic moment is
prabir
is this book for preparing IIT or neet?
is it possible to increase the temperature of a gas without adding heat to it?
I'm not sure about it, but I think it's possible. If you add some form of energy to the system, it's a possibility. Also, if you change the pression or the volume of the system, you'll increase the kinetic energy of the system, increasing the gas temperature. I don't know if I'm correct.
playdoh
For example, if you get a syringe and close the tip(sealing the air inside), and start pumping the plunger, you'll notice that it starts getting hot. Again, I'm not sure if I am correct.
playdoh
you are right for example an adiabatic process changes all variables without external energy to yield a temperature change. (Search Otto cycle)
when a current pass through a material does the velocity varies
lovet
yes at adiabatic compression temperature increase
Nepal
how to draw a diagram of a triode
whate is fckg diagrame?
Arzoodan
why do we use integration?
To know surfaces below graphs.
Jan
To find a Primitive function. Primitive function: a function that is the origin of another
playdoh
yes
Dharmdev
what is laps rate
Dharmdev
Г=-dT/dZ that is simply defination
Arzoodan
what is z
Dharmdev
to find the area under a graph or to accumulate .e.g. sum of momentum over time is no etic energy.
Naod
Z is alt.,dZ altv difference
Arzoodan