Current Electricity

are in parallel and are in parallel and both combinations are in series. So,

Number of units Number of units unit

Applying Kirchhoff's loop rule for the closed loop

As both the wires and are made up of the same metal, therefore their resistivity as well their density are the same
Mass of a wire volume Density
Mass of a wire

where is the density and is the diameter and subscript for wire
Mass of a wire
(Given)



Resistance of wire ,

Resistance of wire ,

Divide by , we get
Using (i))
But (Given)
or

Emf of the battery , emf of supply

Since, the battery is bring changes, so effective emf in the circuit

Current in the circuit



The battery of is being charged by , so the terminal potential across battery of will be greater than its emf.
Terminal potential difference

Here, ,
,


where is the potential gradient across the wire


Internal resistance of the cell is

Number of cell
Number of row
Internal resistance


We know that,

Silver Copper $

When wire of resistance say R is cut into two pieces, its resistance becomes half i.e. R /2. Here equivalent resistance


or

for balanced wheatstone bridge circuit

Given, ,
and
Circuit according to the question,

Net resistance of the circuit,


Current from the battery,
Using in mesh ,

Given, ,
and
Circuit according to the question,

Net resistance of the circuit,


Current from the battery,
Using in mesh ,