Experiments with Circuits, Lenses and Diodes: Quick Revision

A brief note on Experiments with Circuits, Lenses and Diodes. Read it before a practical examination. Try each question at the end before you open its answer.

Circuits

• Ohm's law: the graph of $V$ against $I$ is a line through the origin with the slope $R$. $\rho = \dfrac{R\pi d^2}{4l}$. The ammeter is in series. The voltmeter is across the wire alone.
• Metre bridge: $\dfrac{R}{S} = \dfrac{l}{100 - l}$. The error is least near $l = 50$ cm. Interchange $R$ and $S$ to remove end errors.
• Potentiometer: $V = kl$. $\dfrac{E_1}{E_2} = \dfrac{l_1}{l_2}$ and $r = R\,\dfrac{l_1 - l_2}{l_2}$. The driver emf is larger than the test emf.
• Galvanometer: $G = \dfrac{RS}{R - S}$. Ammeter: $S = \dfrac{I_g G}{I - I_g}$ in parallel. Voltmeter: $R = \dfrac{V}{I_g} - G$ in series.
• Diode: the knee is near $0.7$ V (silicon) and $0.3$ V (germanium). $r_d = \dfrac{\Delta V}{\Delta I}$. Use a series resistor in forward bias.

Light

• Lens and mirror: $\dfrac{1}{f} = \dfrac{1}{u} + \dfrac{1}{v}$. The graph of $\dfrac{1}{v}$ against $\dfrac{1}{u}$ cuts both axes at $\dfrac{1}{f}$. Displacement method: $f = \dfrac{D^2 - d^2}{4D}$.
• Slab: $n = \dfrac{\sin i}{\sin r}$. Lateral shift $d = \dfrac{t\sin(i - r)}{\cos r}$.
• Prism: $n = \dfrac{\sin\frac{A + \delta_m}{2}}{\sin\frac{A}{2}}$. At $\delta_m$, $i = e$.

A worked example

A galvanometer of $75\ \Omega$ gives full deflection for $400\ \mu$A. Make it a voltmeter of $5.0$ V.

1. The total resistance. $\dfrac{V}{I_g} = \dfrac{5.0\ \text{V}}{400 \times 10^{-6}\ \text{A}}$ $= 12\,500\ \Omega$.
2. The series resistor. $R = 12\,500\ \Omega - 75\ \Omega$ $= 12\,425\ \Omega$.

Practise with new numbers

Check yourself

1. A metre bridge balances at $60.0$ cm with a known resistance of $8.0\ \Omega$ in the right gap. What is the unknown resistance?

2. Why is the dynamic resistance of a diode not equal to $V/I$?

3. A prism has an angle of $60^\circ$. At the least deviation, the angle of incidence is $50^\circ$. What is the least deviation?

Sources

• NCERT, Laboratory Manual: Physics, Class XII.
• NCERT, Physics Class XII, Chapters 3, 4, 9 and 14.
• OpenStax University Physics Volumes 2 and 3.