Two identical resistors, each of resistance , are connected in (i) series, and (ii) parallel, in turn to a battery of . Calculate the ratio of the power consumed in the combination of resistors in each case.
Step 1: Calculation of equivalent resistance while connected in series
The equivalent resistance of the resistors when connected in series can be found as follows:
Where is the equivalent resistance, and is the resistance of the resistors.
Step 2: Calculation of equivalent resistance while connected in parallel
The equivalent resistance of the resistors when connected in parallel can be found as follows:
Step 3: Calculation of power in both the cases
The equation of power can be expressed as follows:
Where, is the power, and is the voltage.
2. Power while the connection is in parallel
3. Calculation of ratio of powers
Therefore, the ratio of powers is .