Compare the power used in the 2 Ohm resistor in each two different circuits.

Ques. Compare the power used in the 2 ohms resistor in each of the following circuits:
(i) a 6 V battery in series with 1 ohm and 2 ohms resistor, and
(ii) a 4V battery in parallel with 12 ohms and 2 ohms resistors.

Solution:

In order to compare the power that is used in the two combinations, we have:

• Potential difference: V1 = 6V, Resistance values, R1 = 1 Ohm, and R2 = 2 Ohm 
• Potential difference: V2 = 4V, Resistance values, R3 = 12 Ohm, and R4 = 2 Ohm 

(i) 6V battery (series combination) with 1 Ohm and 2 Ohms Resistors

As per question, the given values are:

• The potential difference of the given battery = 6 V
• Resistors connected in Series = 1 Ohm and 2 Ohm

The formula for equivalent resistance in the given series combination is calculated as: 

R_eq=R₁+R₂

Here, R₁= 1 Ohm, R₂= 2 Ohm

The equivalent resistance will be,

R = 1 + 2 = 3 Ohm

Now, as per Ohm’s law,

Here, I is the current through the circuit

Thus, I = 6/3

⇒ I = 2 A

This is the flow of current via each component of the circuit since there is no division of current in series combination circuits. Therefore, the flow of current through the 2 Ohm resistor equals 2 A.

Power can be expressed by, P= I²R

Thus, P = 2²× 2

⇒ P = 8 W

Thus, the total power consumed by the two resistors will be 8 Watts. 

(ii) 4V Battery Parallelly Connected with 12 Ohm and 2 Ohm Resistors

As per question, the given values are:

• The potential difference of the given battery, = 4 V
• Resistors connected in Parallel = 12 Ohm and 2 Ohm 

Note: The voltage across each component in a parallelly connected circuit remains the same. Therefore, the voltage across the 2 Ohm resistor is going to be 4V.
The power used in the 2-ohm resistor is expressed by: P = V²/R

⇒ P = 4²/2

⇒ P = 8 W

Thus, the power consumed by a 2 Ohm resistor in both cases is 8 W.

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