Use a null ratio to isolate internal resistance

A cell balances against 90 cm of a uniform potentiometer wire while unloaded. With a 6 Ω resistor across the cell terminals, the balance length becomes 60 cm. The driver maintains the same potential gradient in both measurements.

What internal resistance follows from this model?

Organize the givens & assumptions

Unloaded balance: 90 cm
Loaded balance: 60 cm
External load: 6 Ω

Constant ideal emf and positive Ohmic internal resistance over the stated interval; settled DC currents and negligible lead resistance. This is an assigned source model, not battery test data. Ideal detector null; uniform wire and unchanged driver gradient. The null branch draws no current; the separate load draws current in the loaded measurement.

A $0\ \Omega$
B $3\ \Omega$
C $9\ \Omega$
D $4\ \Omega$

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