TEST OF PRACTICAL KNOWLEDGE QUESTION You have been provided with a resistance box, a voltmeter, a key, a battery, and other necessary materials. Connect the...

Answer Details

(a) EMF / internal-resistance experiment (outline). With the resistance box set to \(R\), the voltmeter reads the terminal p.d. \(V\) across it. Since \(V = \dfrac{ER}{R + r}\) (where \(E\) is the e.m.f. and \(r\) the internal resistance), taking reciprocals gives

Plotting \(V^{-1}\) (vertical) against \(R^{-1}\)... equivalently against \(R\) as directed, the intercept \(C\) on the \(V^{-1}\) axis gives \(\dfrac{1}{E}\), so \(E = C^{-1}\); the slope together with the intercept yields the internal resistance \(r\).

Precautions: use the voltmeter of high resistance and read it at eye level (avoid parallax); close the key only while taking readings so the cell is not run down, and ensure firm, clean connections.

(b)(i) Potential difference between two points is the work done in moving unit positive charge from one point to the other in the circuit (energy converted per unit charge).

(b)(ii) The e.m.f. is the total energy supplied per unit charge by the cell. When the cell drives current \(I\) through an external resistance, some energy is lost inside the cell across its own internal resistance \(r\) (a "lost volt" \(Ir\)). Hence the p.d. across the terminals, \(V = E - Ir\), is less than the e.m.f. \(E\); they are equal only when no current flows.