10.6 Household Wiring and Electrical Safety

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?

What voltage is involved in a 1.44-kW short circuit through a $0.100 - \Omega$ resistance?

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 $4000 \Omega$. What is the smallest voltage on the case of the radio that could cause ventricular fibrillation?

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

A heart defibrillator passes 10.0 A through a patient’s torso for 5.00 ms in an attempt to restore normal beating. (a) How much charge passed? (b) What voltage was applied if 500 J of energy was dissipated? (c) What was the path’s resistance? (d) Find the temperature increase caused in the 8.00 kg of affected tissue.

A circuit contains a D cell battery, a switch, a $20 - \Omega$ resistor, and four 20-mF capacitors connected in series. (a) What is the equivalent capacitance of the circuit? (b) What is the RC time constant? (c) How long before the current decreases to $50 \%$ of the initial value once the switch is closed?

A student makes a homemade resistor from a graphite pencil 5.00 cm long, where the graphite is 0.05 mm in diameter. The resistivity of the graphite is $\rho = 1.38 \times 10^{−5} \Omega / \text{m}$. The homemade resistor is place in series with a switch, a 10.00-mF uncharged capacitor and a 0.50-V power source. (a) What is the RC time constant of the circuit? (b) What is the potential drop across the pencil 1.00 s after the switch is closed?

Three $300 - \Omega$ resistors are connect in series with an AAA battery with a rating of 3 AmpHours. (a) How long can the battery supply the resistors with power? (b) If the resistors are connected in parallel, how long can the battery last?

Two resistors, one having a resistance of $900 \text{k} \Omega ,$ are connected in series to produce a total resistance of $0.500 \text{M} \Omega$. (a) What is the value of the second resistance? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?

Apply the loop rule to Loop akledcba in the preceding problem.

A $160 - \mu \text{F}$ capacitor charged to 450 V is discharged through a $31.2 -\text{k} \Omega$ resistor. (a) Find the time constant. (b) Calculate the temperature increase of the resistor, given that its mass is 2.50 g and its specific heat is $1.67 \text{kJ}/\text{kg} \cdot ° \text{C} ,$ noting that most of the thermal energy is retained in the short time of the discharge. (c) Calculate the new resistance, assuming it is pure carbon. (d) Does this change in resistance seem sig…

A 120-V immersion heater consists of a coil of wire that is placed in a cup to boil the water. The heater can boil one cup of $20.00 ° \text{C}$ water in 180.00 seconds. You buy one to use in your dorm room, but you are worried that you will overload the circuit and trip the 15.00-A, 120-V circuit breaker, which supplies your dorm room. In your dorm room, you have four 100.00-W incandescent lamps and a 1500.00-W s…