Two resistors R1 and R2 (where R1 has twice the resistance of R2, R1=2R2) are co

Question

Two resistors R1 and R2 (where R1 has twice the resistance of R2, R1=2R2) are connected, along with a battery, in two arrangements as shown. An identical potential difference V across the battery produces a current I in each circuit (note the current I is different in each circuit).

R2 R2 For each circuit fill in the blanks below to show the relations between the currents and potential differences in each resistor. Connection Tsp: Current (in terms of I) Ry: Potential Difference (in terms of V) 2-

Explanation / Answer

first figure

connection type : series

current through R1 = I

current through R2 = I

potentail difference across R1 = V*R1/(R1+R2) = V*R1/(R1 + R1/2) = (2/3)*V

potentail difference across R2 = V*R2/(R1+R2) = V*R2/(2*R2+ R2) = (1/3)*V

second figure

connection type : parallel

current through R1 = I*R2/(R1+R2) = I*R2/(2*R2 + R2) = (1/3)*I

current through R2 = I*R1/(R1+R2) = I*R1/(R1 + R1/2) = (2/3)*I

potentail difference across R1 = V

potentail difference across R2 = V

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