Final answer:
In a meter bridge circuit with a balance length of 50 cm connected to a known 30 ohm resistance, the unknown resistance is also calculated to be 30 ohms because the length ratio suggests that the two resistances must be equal.
Step-by-step explanation:
Calculating Unknown Resistance in a Meter Bridge Circuit
The meter bridge, also known as a Wheatstone bridge, is used here to determine an unknown resistance. Given that the balance length is 50 cm (which implies the bridge is balanced), and it is connected to a fixed 30 ohm resistance, we can use the principle of the Wheatstone bridge to find the unknown resistance.
The balance condition for a Wheatstone bridge can be expressed in the form of a ratio:
R1/R2 = R3/R4
Where 'R1' is the known fixed resistance (which is 30 ohms in this case), 'R2' is the unknown resistance, 'R3' and 'R4' are the resistances of the two branches which are in proportion to the length of the bridge (here, 'R3' corresponds to the balance length of 50 cm, so 'R4' would be 100 cm - 50 cm = 50 cm as well).
Since 'R3/R4' is 50/50 or 1, and 'R1' is 30 ohms, we can set up the equation:
30 ohms / Unknown Resistance = 1
Solving for the unknown resistance gives us that it is also 30 ohms.