Question

i)Compare the power used in the 2Ω resistor in each of the following circuits:

a) a 6V battery in series with 1Ω and 2Ω resistor.

b) a 4V battery in parallel with 12Ω and 2Ω resistor. ​

Answer 1

Answer:

.

We need to compare the power consumed in the given two combinations.

(i) Given

A 6 V battery in series with 1 Ohm and 2 Ohm resistors

Potential difference, V = 6 V

1Ohm and 2 Ohm resistors are connected in series.

Therefore, the equivalent resistance of the circuit,

R = 1 + 2 = 3 Ohm

According to Ohm’s law,

V = IR

Where,

I is the current through the circuit

I= 6/3 = 2 A

This current will flow through each component of the circuit because there is no division of current in series circuits. Hence, the current flowing through the 2Ohm resistor is 2 A.

Power is given by the expression,

P= I^2R =

2^2X 2 = 8 W

(ii) Given

A 4 V battery in parallel with 12 Ohm and 2 Ohm resistors.

Potential difference, V = 4 V

12 Ohm and 2 Ohm resistors are connected in parallel.

The voltage across each component of a parallel circuit remains the same. Hence, the voltage across 2 Ohm resistor will be 4 V.

Power consumed by 2 Ohm resistor is given by

P= V^2/R = 4^2/2 = 8 W

Therefore, the power used by 2 Ohm resistor is 8W.