Three identical resistors are connected in series. When a certain potential difference is applied across the combination, the total power dissipated is 18.0 W. What power would be dissipated if the three resistors were connected in parallel across the same potential difference?
Identical? If in parallel, instead of the resistance 3R in series, the resistance will be R/3. So total current will be nine times as much, at the same voltage.
What does that tell you about power?
Identical? If in parallel, instead of the resistance 3R in series, the resistance will be R/3. So total current will be nine times as much, at the same voltage.
What does that tell you about power?
If the potential remains the same, then according to the equation I = PV, the power would also be nine times as much. Thanks so much for your help!
You're welcome! I'm glad I could help. Yes, you are correct. When the three identical resistors are connected in parallel, the total resistance becomes R/3. Since the potential difference across the combination remains the same, the total current flowing through the circuit will be nine times as much as when the resistors were in series (since resistance and current are inversely proportional according to Ohm's Law).
Now, when it comes to power, the equation P = IV tells us that power is directly proportional to both current (I) and voltage (V). Since the current increases by a factor of nine when the resistors are in parallel, the power dissipated will also increase by a factor of nine (assuming the potential difference remains constant).
Therefore, if the total power dissipated when the resistors are in series is 18.0 W, when the resistors are connected in parallel across the same potential difference, the power dissipated will be 9 times 18.0 W, which is 162.0 W.