Resistance

Here: resistance of galvanometer Maximum current across galvanometer Current range in ammeter = 10 A Since, the shunt resistance should be connected in parallel to convert the galvanometer into an ammeter.

Using Ohm’s law, which states: Where: - is the current, - is the resistance. Now, substitute the values: Thus, the potential difference across the conductor is .

Concept:
When resistors are connected in parallel, the reciprocal of the equivalent resistance is equal to the sum of the reciprocals of the individual resistances. ::contentReference[oaicite:0]{index=0}

Step 1: Write the given resistance values.

Step 2: Substitute the values in the parallel resistance formula.

Step 3: Calculate the equivalent resistance. Hence, the equivalent resistance is:

Concept: Resistance of a wire is given by When the wire is stretched, its volume remains constant.

Step 1: Determine the new length. Since volume is constant,

Step 2: Find the new resistance.

Concept: A cube has 12 identical resistors . When resistance is measured between opposite corners, symmetry can be used to simplify the circuit. All three vertices adjacent to the first corner are at the same potential, and similarly the three vertices adjacent to the opposite corner are at another common potential. Thus the circuit reduces to a simpler combination of series and parallel resistances.
Step 1: {Group symmetric points.} Let the opposite corners be and . Due to symmetry: - The three vertices connected to have equal potential. - The three vertices connected to also have equal potential. Thus the cube effectively reduces to three resistors from to the first group.
Step 2: {Find equivalent resistance from to the first symmetric group.} Three resistors are in parallel:
Step 3: {Resistance between the two middle groups.} There are six resistors connecting these groups, all in parallel:
Step 4: {Resistance from the second group to .} Again three resistors in parallel:
Step 5: {Add series resistances.}

Concept: Resistance of a wire is given by where = resistivity, = length of wire, = cross-sectional area. When a wire is stretched, its volume remains constant.

Step 1: Apply the change in length. Initial length: Final length: Using constant volume:

Step 2: Calculate the new resistance. Initial resistance: Final resistance: Substitute :

Step 3: Final result.