Question

derive internal resistance

Answer 1

Consider the circuit given below. The cell can be modified with an emf ε and the internal resistor with resistance r which is connected in series. An external load resistor with resistance R is also connected across the circuit. The terminal potential difference represented as V is defined as the potential difference developed between the positive and negative terminals of the cell when current flows through the circuit.

V = V+ + V- – Ir. This is the voltage drop accomplished due to the internal resistance.

We know that ε = V+ + V-. = I (R + r).

ε = IR + Ir.

= V + Ir

V = ε – Ir.

So, V = ε – Ir, where V is the potential difference across the circuit, ε is the emf, I is the current flowing through the circuit, r is internal resistance.  

Answer 2

internal resistance:

v = e -ir

r = ev/i

i = v/R

r =R{ e/v-i}

when k is open

e= l1

when k is closed

v=l2

e/v = l1/l2

so hence , r = R{l1/l2 - i }