Resistance And Resistivity

The given circuit is a symmetric triangle, where each side has a resistance of . We need to find the effective resistance between points A and B.
Step 1: Resistors in Series
Each set of two resistors in series will give:
Step 2: Resistors in Parallel
The three resistors are now in parallel. Using the formula for resistors in parallel: Thus, the effective resistance is:
Step 3: Substituting the value of
Given that , we have:

Concept: In a Wheatstone bridge:

If the bridge is balanced → no current flows through the central branch
Balance condition:

Step 1: Identify resistances. From the figure:

Left upper arm =
Left lower arm =
Right upper arm =
Right lower arm =
Central branch =

Step 2: Check bridge balance. Bridge is not perfectly balanced. But simplify ratios: Still not equal → not balanced.
Step 3: However, note symmetry in supply. The 6 V battery is connected across left and right nodes. The bridge can be analyzed by simplifying two parallel series branches: Upper path resistance: Lower path resistance:
Step 4: Potential at junctions. Let total voltage = 6 V. Voltage division in upper branch: Current in upper branch: Voltage drop across 20Ω: Lower branch current: Voltage at lower junction:
Step 5: Compare junction potentials. Almost equal → potential difference across 3Ω is negligible. Conclusion: Potential difference across the central branch is nearly zero, so no current flows through the resistor. Final Answer:

Concept: Resistance variation with temperature: Where:

= temperature coefficient of resistance


Step 1: Given data.
Step 2: Use linear relation.
Step 3: Solve for . Final Answer:

Concept: A Wheatstone bridge is used to compare resistances. It consists of four resistors arranged in a diamond shape with a galvanometer between the middle junctions. Let the four resistances be:
Step 1: Bridge configuration.

and in one branch
and in the other branch
Galvanometer connected between junctions B and D
Bridge is balanced when no current flows through galvanometer.
Step 2: Condition for balance. If no current flows through galvanometer:

Potential at junction B = potential at junction D
So:
Step 3: Using potential division. Current through branch = Current through branch = Potential at B (between and ): Potential at D (between and ): For balance:
Step 4: Total potential drop in branches. Since both branches are across the same battery:
Step 5: Divide (1) by (2).
Step 6: Simplify. Cross multiplying: Final Condition: This is the condition for a balanced Wheatstone bridge. Conclusion: When the ratio of resistances in one branch equals the ratio in the other branch, no current flows through the galvanometer and the bridge is balanced.

Concept: Resistivity of a material is given by: Where:

= resistance of wire
= cross-sectional area
= length of wire
Also, from Ohm’s law:
Step 1: Calculate resistance.
Step 2: Convert area into SI units.
Step 3: Substitute into resistivity formula. Final Answer:

Concept: For an electrical appliance:

Power relation:
Heat produced:

Step 1: Given data.
Step 2: Find resistance of iron. Using:
Step 3: Operated at 110 V. New power consumed:
Step 4: Heat produced in 10 minutes. Time: Final Answers:

[(i)] Resistance =
[(ii)] Heat produced =