All answers need to be supported by specific data from previous investigations!

Question

All answers need to be supported by specific data from previous investigations! Shown in the figure at the right are two resistors connected in parallel with a battery. The current through the top resistor is three times the current through the bottom resistor. l) If each resistor was connected by itself to the battery, how would the current through each compare to the other? Explain fully and give evidence 2) If the two resistors were connected in series with the battery, how would the currents through each compare to the other? Explain fully and give evidence.

Explanation / Answer

The resistance are connected in parallel. The voltage across each resistance will be equal (say V)
Let the resistance of the first resistance be R1and that of the second be R2
The resistance R1 = V / I1  
and R2 = V / I2 ---------------------- 1
The current through the first resistor is three times the current through the second resistor
I1 = 3 I2
R1 = V / 3 I2  ----------------2
Dividing 1 by 2
R2/ R1 = 3
The bottom resistor is equal to three timee times the top resistor
R2 = 3 R1
1) Each resistor is connected to the battery
The current through the resistor R1 is
I1 = V/ R1
The current through the resistor R2 is
I2  = V / R2
Using the relation between R1and R2
I1 / I2 = 3
The current through the first resistor is equal to three times the current through the second resistor
2) If the two resistors are connected in series, the voltage across the resistors will be different but the current will be the same
The current through the first resistor will be equal to that of the current through the second resistor
3) For the parallel resistors, the total current from the battery is
Ip = V / Req
Ip   = V / (R1 R2 / R1 + R2 )
Using the relation R2 = 3 R1
Ip  = V / (3R1/4 )
Ip   = 4 V / 3 R1
For the series circuit
Is = V / Req
The equivalent resistance is
Req = R1 + R2  = 4 R1
Is  = V / 4 R1
Ip / Is   = 16/ 3
Thus the current from the battery in the parallel circuit is (16/3) times that of the current from the battery in the series circuit

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