2. In the figure below, what is the net resistance of the circuit connected to the battery? Each resistance in the circuit is equal to 3.20 k2. 19 0of19
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The resistance of each resistor is given as,
The resistance in series can be determined as,
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- When a straight wire is heated, its resistance changes according to the equation R = R0 [1 + (T T0)] (Eq. 17.7), where is the temperature coefficient of resistivity. (a) Show that a more precise result, which includes the length and area of a wire change when it is heated, is R=R0[1+(TT0)][1+(TT0)][1+2(TT0)] where is the coefficient of linear expansion. (See Topic 10.) (b) Compare the two results for a 2.00-m-long copper wire of radius 0.100 mm, starting at 20.0C and heated to 100.0C.A physics student uses a 115.00-V immersion heater to heat 400.00 grams (almost two cups) of water for herbal tea. During the two minutes it takes the water to heat, the physics student becomes bored and decides to figure our the resistance of the heater. The student starts with the assumption that the water is initially at the temperature of the room Ti=25.00C and reaches Tf=100.00C . The specific heat of the water is c=4180JkgK What is the resistance of the heater?SPEAR, a storage ring about 72.0 m in diameter at the Stanford Linear Accelerator (closed in 2009), has a 20.0-A circulating beam of electrons that are moving at nearly the speed of light. (See Figure 20.39.) How many electrons are in the beam? Figure 20.39 Electrons circulating in the storage ring called SPEAR constitute a 20.0-A current. Because they travel close to the speed of light, each electron completes many orbits in each second.
- Knowing that the severity of a shock depends on the magnitude of the current through your body, would you prefer to be in series or parallel with a resistance, such as the heating element of a toaster, if shocked by it? Explain.An automobile starter motor has an equivalent resistance of 0.0500 and is supplied by a 12.0-V battery with a 0.0100- internal resistance, (a) What is the current to the motor? (b) What voltage is applied to it? (c) What power is supplied to the motor? (d) Repeat these calculations for when the battery connections are corroded and add 0.0900 to the circuit. (Significant problems are caused by even small amounts of unwanted resistance in low-voltage, high-current applications.)The circuit in Figure P27.34a consists of three resistors and one battery with no internal resistance. (a) Find the current in the 5.00- resistor. (b) Find the power delivered to the 5.00- resistor. (c) In each of the circuits in Figures P27.34b, P27.34c, and P27.34d, an additional 15.0-V battery has been inserted into the circuit. Which diagram or diagrams represent a circuit that requires the use of Kirchhoffs rules to find the currents? Explain why. (d) In which of these three new circuits is the smallest amount of power delivered to the 10.0- resistor? (You need not calculate the power in each circuit if you explain your answer.) Figure P27.34
- Integrated Concepts (a) An immersion heater utilizing 120 V can raise the temperature of a 1.00 102 -g aluminum cup containing 350 g of water from 20.0°C to 95.0°C in 2.00 min. Find its resistance, assuming it is constant during the process. (b) A lower resistance would shorten the heating time. Discuss the practical limits to speeding the heating by lowering the resistance.A battery-operated car uses a 12.0-V system. Find the charge the batteries must be able to move in order to accelerate the 750 kg car from rest to 25.0 m/s, make it climb a 2.00102 -in high hill, and finally cause it to travel at a constant 25.0 m/s while climbing with 5.00102 -N force for an hour.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°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 nip 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 space heater, (a) What is the power rating of the immersion heater? (b) Will it trip the breaker when everything is turned on? (c) If it you replace the incandescent bulbs with 18.00-W LED, will the breaker nip when everything is turned on?
- Consider the circuits shown below, (a) What is the current through each resistor in part (a)? (b) What is the current through each resistor in part (b)? (c) What is the power dissipated or consumed by each circuit? (d) What is the power supplied to each circuit?The label or a portable radio recommends the use of rechargeable nickel-cadmium cells (nicads), although they have a 1.25-V emf while alkaline cells have a 1.58-V emf. The radio has a 3.20- resistance, (a) Draw a circuit diagram ot the radio and its batteries. Now, calculate the power delivered to the radio, (b) When using Nicad cells each having an internal resistance of 0.0400O. (c) When using alkaline cells each having an internal resistance of 0.200 . (d) Does this difference seem significant, considering that the radio s effective resistance is lowered when its volume is turned up?Integrated Concepts (a) Assuming 95.0% efficiency for the conversion of electrical power by the motor, what current must the 12.0-V batteries of a 750-kg electric car be able to supply: (a) To accelerate from rest to 25.0 m/s in 1.00 min? (b) To climb a 2.00 102-m- high hill in 2.00 min at a constant 25.0-m/s speed while exerting 5.00 102 N of force to overcome air resistance and friction? (c) To travel at a constant 25.0-m/s speed, exerting a 5.00 102 N force to overcome air resistance and friction? See Figure 20.44.