A 12-V battery is connected to terminals A and B in the above Figure.(a) Given that R = 75 ohms, find the current in each resistor.(b) Suppose the value of R is increased. For each resistor in turn, state whether the current flowing through it increases or decreases. Explain.

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opsadnojD · Accepted Answer

You have two resistors in parallel, 55 and 75, and then these are together in series with the 12. So first combine the two in parallel:  Req=R1R2R1+R2=55⋅75130=31.73 ohms  Now add this to the 12 ohm resistor in series: 43.73 ohms  This is the total resistance for the circuit. Find the total current for the circuit:  V=IR or I=V/R=12 volts/43.73 ohms=0.274amps  You know all of this current must go through the 12 ohm resistor (although the current splits between the other two in parallel). So find the potential (voltage) across the 12 ohm resistor:  V=IR=(0.274 A)(12ohms)=3.29 Volts  So if the difference between one side and the other is 3.29volts, and the difference from a to b is 12 volts, then the difference from one side of the 75 ohm resistor and the other must be:  12-3.29=8.71 Volts.  Now you can find the current through the 75 ohm resistor,using ohms law:  i=V/R=8.71 Volts/75 ohm=0.116 A  Note that the rest of the current:0.274 -0.116 = 0.158 A goes through the otherresistor.  Now for part b: if the resistance of R is increased...  less current goes through the 12 ohm resistor, because the overall resistance of the circuit is increased so there is less total current.  less current goes through the R resistor, because its resistance is increased.  Although there is less overall current, a greater fraction of the total current will go through the 55 ohm resistor and the current through this one will actually increase!

A 12-V battery is connected to terminals A and B in the above Figure.(a) Given that R = 75 ohms, find the current in each resistor.(b) Suppose the value of R is increased.

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