For the circuit shown in FIGURE , find the current through and the potential difference across each resistor. Place your results in a table for ease of reading.
We have given the circuit.
We need to find the current through and the potential difference across each resistor.
When the resistors are connected at both the ends of the point then it is said that the resistors are connected in parallel. This is obvious when the resistors are aligned side by side. The potential difference across the resistors is the same in parallel connection. Equation shows the equivalent resistance for the parallel connection in the form
The two resistors and are in parallel, so we use the equation to get their combination by
The resistor is in series with a combination ,so they have the same current. We apply the loop rule to get the current through resistors and the combination . Traveling clockwise in the left loop and get the next
Appling the loop rule on the right loop and travel clockwise to get
The current from the junction rule equals .Use this into equation to get by
Hence, the current through is
Using Ohm's law to get the voltage across both resistors by
The current is the same for resistors , so the current through it is calculated by
Use Ohm's law to get the voltage across this resistor by
Both resistors and have the same voltage and their combination current is the same for , so using Ohm's law, the voltage across both of them is
Again using Ohm's law, the current through and will be
The results are summarised in below's table
A circuit you’re building needs an ammeter that goes from to a full-scale reading of . Unfortunately, the only ammeter in the storeroom goes from to a full-scale reading of only . Fortunately, you’ve just finished a physics class, and you realize that you can make this ammeter work by putting a resistor in parallel with it, as shown in FIGURE P28.57. You’ve measured that the resistance of the ammeter is, not theof an ideal ammeter.
a. What value of R must you use so that the meter will go to full scale when the current I is?
b. What is the effective resistance of your ammeter?
A string of holiday lights can be wired in series, but all the bulbs go out if one burns out because that breaks the circuit. Most lights today are wired in series, but each bulb has a special fuse that short-circuits the bulb—making a connection around it—if it burns out, thus keeping the other lights on. Suppose a string of lights is connected in this way and plugged into a outlet. By what factor does the power dissipated by each remaining bulb increase when the first bulb burns out?
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