Answer :
For two resistor circuits, in a series circuit with a 6 V battery, a 1
resistor uses 4 W while a 2
resistor uses 8 W. In a parallel circuit with a 4 V battery, a 12
resistor uses 1.33 W and each 2
resistor uses 8 W, showing that 2
resistors use more power in both types of circuits.
When comparing the power used in the 2-resistor circuits, the first step is to understand the difference between series and parallel connections. In a series circuit, the total voltage supplied by the battery is shared among the resistors. Conversely, in a parallel circuit, the voltage across each resistor is the same as the voltage of the battery.
(i) In the series circuit with a 6 V battery, and 1 and 2
resistors, the total resistance (Rt) is Rt = 1
+ 2
= 3
. The current (I) through the circuit can be calculated using Ohm's Law (V = IR), giving I = 6 V / 3
= 2 A. The power dissipated by each resistor is P = I^2
* R, thus:
- For the 1
resistor: P = (2 A)^2 * 1
= 4 W - For the 2
resistor: P = (2 A)^2 * 2
= 8 W
(ii) In the parallel circuit with a 4 V battery, and 12
, 2
, and 2
resistors, each resistor gets the full battery voltage. The power dissipated can be found with P = V^2 / R, so:
- For the 12
resistor: P = (4 V)^2 / 12
= 1.33 W - For each 2
resistor: P = (4 V)^2 / 2
= 8 W
The computation reveals that in both the series and parallel circuits, the 2
resistors use more power than the 1
or 12
resistors, respectively, due to the direct relationship between power and resistance when the current (in series) or voltage (in parallel) is fixed.
