Question

A resistor of unknown resistance and a 22 Ω resistor are connected across a 20 V emf in such a way that a 2.0 A current is observed in the emf. What is the value of the unknown resistance?

Answer 1

Given data in the problem :

Unknown resistance = R1 (say)

Known resistance = R2 = 22 Ω

Potential difference (Source of emf) = 20 Volts

Current through the circuit is 2 Amps

Now in the problem its just stated that the two resistors are just connected but its not told that whether its a series or a parallel connection. To solve this we need to know the following

If the equivalent resistance of the circuit is greater than the known resistance , then Series connection

If the equivalent resistance of the circuit is smaller than the known resistance , then Parallel connection

Now lets calculate the equivalent resistance of the circuit :

Simply by ohm's law ,

from V=IR,

R=v/I = 20/2 = 10 Ω

But R2 = 22 Ω  

Thus the mode of connection must be Parallel connection (Since 10 Ω < 22 Ω )

Applying the formula for Parallel connection

1/R = 1/R1 + 1/R2

1/10 = 1/R1 + 1/22

22 R = 220 + 10 R

12 R =220

R=18.333 Ω  

Therefore ,

the value of the unknown resistance (R1) is 18.333 ohms.