V. Additional practice 1. A group is considering the following circuit. Three re

Question

V. Additional practice 1. A group is considering the following circuit. Three resistors are connected as shown in a circuit with a 12 volt battery. The resistances are: 12 V Rc is of unknown value (larger than 0) A. Andy thinks RA has the most current going through it. A. J. says that it is impossible to determine unless the value of Rc is known. Who do you agree with? Explain your reasoning B. Rank the resistors based on the potential difference across them, from largest to smallest. Justify your choices. C. If Rc is increased, what happens to the currents through the different elements of the circuit? i. The current through the battery ii. The current through RA.

Explanation / Answer

A. Whatever the value of resistance is of RC, the current through resistor RA will be equal to current in circuit. And the current will then divide between resistors RB and RC based on their values. But whatever the case be, current in resistor RC will be less than RA . Therefore, Andy is thinking correctly.

B. Since resistors RB and RC are in parallel, the potential difference across them will always be equal

Also, value of RA is equal to 4Ohms and that of RB is 3 Ohms . Whatever the value of RC , the equivalent resistor of RB and RC will always be less than 3 Ohms and hence the equivalent resistance of RB and RC will always be less than RA . Therefore, potential across RA will be higher than RB (or RC for that matter). Therefore, arranging the resitors from largest to smallest potential drops ,the order is RA> RB=RC

C. When RC is kept increasing the equivalent resitance of the circuit keeps increasing. Therefore, circuit current keeps reducing.

i)Current through battery keep reducing

ii)The current through RA keeps reducing

  

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