Question

Study the following circuit:

On the basis of this circuit, answer the following questions:

i. Find the value of total resistance between the points A and B.

ii. Find the resistance between the points B and C.

iii. Calculate the current drawn from the battery, when the key is closed

OR

iii. In the above circuit, the 16Ω resistor or the parallel combination of two resistors of 8 Ω, which one of the two will have more potential difference across its two ends? Justify your answer.

Answer 1

i. To find the total resistance between points A and B, we simply add up the resistances in series:

R_AB = R_4Ω + R_6Ω + R_16Ω = 4Ω + 6Ω + 16Ω = 26Ω

ii. The resistance between points B and C is a bit more complex because we have two resistances in parallel. We use the formula for resistances in parallel:

`1/R_(BC)=1/R_(8Ω,upper)+1/R_(8Ω,lower)`

`1/R_(BC)=1/(8Ω)+1/(8Ω)= 1/(4Ω)`

`R_(BC) = 4Ω`

iii. To calculate the current drawn from the battery when the key is closed, we need to find the total resistance in the circuit. The total resistance will be the sum of the resistance between A and B and the equivalent resistance between B and C which we found to be

R_AB + R_BC = 26Ω + 4Ω = 30Ω

Now, using Ohm's Law (V=IR), where V is the voltage of the battery, I is the current, and R is the total resistance, we can find the current:

`I = V/R = (6V)/(30Ω) = 0.2 A`

So, the current drawn from the battery is 0.2 A (or 200 mA).

OR

iii. The potential difference across a resistor in a circuit is given by Ohm's Law, which states:

V = I.R

where V is the potential difference, I is the current, and R is the resistance.

In the given circuit, the 16Ω resistor is in series with two other resistors (4Ω and 6Ω), and the combination of two 8Ω resistors is in parallel. The total resistance in series (4Ω + 6Ω + 16Ω = 26Ω) is greater than the effective resistance of the parallel combination of two 8Ω resistors which is 4Ω, since resistors in parallel have an effective resistance R_parallel​ given by

`1/R_("parallel")=1/R_1+1/R_2`

Therefore, the series combination (including the 16Ω resistor) has more resistance than the parallel combination, which means it will have more potential difference across it. Since the same current flows through the series resistors, the potential difference across the 16Ω resistor will be the largest among the individual resistors because it has the highest resistance.

So, the 16Ω resistor will have more potential difference across its ends than the parallel combination of two 8Ω resistors.