Question

Study the circuit shown in which two resistors X and Y of resistances 3 Ω and 6 Ω respectively are joined in series with a battery of 2 V.

1. Draw a circuit diagram showing the above two resistors X and Y joined in parallel with the same battery and the same ammeter and voltmeter.  (1)
2. In which combination of resistors will the (i) potential difference across X and Y and (ii) current through X and Y, be the same?  (1)
3. 1. Find the current drawn from the battery by the series combination of the two resistors (X and Y).  (2)
      OR
   2. Determine the equivalent resistance of the parallel combination of the two resistors (X and Y).  (2)

Answer 1

I.

II. In which combination of resistors will: 

1. In the parallel combination, the potential difference across both resistors (X and Y) is the same.
2. In the series combination, the current through both resistors is the same. 

III. a.

Given: 

Resistance of X = 3 Ω

Resistance of Y = 6 Ω

Battery voltage = 2 V

Find the total current using Ohm's Law:

`"R"_"series"​ = "R"_"X" ​+ "R"_"Y"`

= 3 Ω + 6 Ω

= 9 Ω

Find the total current using Ohm's Law: 

`I = V/R`

= `(2V)/(9Ω)`

= 0.22 A

OR

b. Formula for parallel resistance:

`1/(R_"parallel") = 1/(R_X) + 1/(R_Y)`

`1/(R_"parallel") = 1/3 + 1/6`

`1/(R_"parallel") = 2/6 + 1/6`

`1/(R_"parallel") = 3/6`

`1/(R_"parallel") = 1/2`

`"R"_"parallel"` = 2 Ω