(i) What is dielectric? (ii) A parallel plate capacitor consists of two plates each of area 9.6 x 10\(^{-2}\)m\(^2\), separated by a dielectric of thickness...

(a)(i) Dielectric

A dielectric is an insulating material (solid, liquid or gas) placed between the two plates of a capacitor. When placed in the field it becomes polarised and increases the capacitance of the capacitor. Examples are mica, waxed paper and air.

(a)(ii) Capacitance

\[ C = \frac{\varepsilon_r\,\varepsilon_0\,A}{d} \]

with \(\varepsilon_r = 900\), \(\varepsilon_0 = 8.85\times10^{-12}\,\text{Fm}^{-1}\), \(A = 9.6\times10^{-2}\,\text{m}^2\) and \(d = 2.25\times10^{-3}\,\text{m}\):

\[ C = \frac{900 \times 8.85\times10^{-12} \times 9.6\times10^{-2}}{2.25\times10^{-3}} = 3.4\times10^{-7}\,\text{F} \]

(b)(i) Ammeter or voltmeter?

The voltmeter has the higher resistance. A voltmeter is connected in parallel with the component whose p.d. is being measured, so it must have a very high resistance to draw only a negligible current and avoid disturbing the circuit. An ammeter is connected in series and must have a very low resistance so that it does not alter the current it measures.

(b)(ii) Voltmeter reading

The two 400 \(\Omega\) resistors on the left are in parallel:

\[ \frac{1}{R_1} = \frac{1}{400} + \frac{1}{400} \Rightarrow R_1 = 200\,\Omega \]

The 800 \(\Omega\) resistor is in parallel with the 800 \(\Omega\) voltmeter:

\[ \frac{1}{R_2} = \frac{1}{800} + \frac{1}{800} \Rightarrow R_2 = 400\,\Omega \]

\(R_1\) and \(R_2\) are in series across the 6 V supply:

\[ R_T = 200 + 400 = 600\,\Omega, \qquad I = \frac{V_T}{R_T} = \frac{6}{600} = 0.01\,\text{A} \]

The voltmeter reads the p.d. across \(R_2\):

\[ V = I\,R_2 = 0.01 \times 400 = 4.0\,\text{V} \]

(c) Equivalent resistance

The two 2 \(\Omega\) resistors in parallel combine to:

\[ \frac{1}{R_p} = \frac{1}{2} + \frac{1}{2} = 1 \Rightarrow R_p = 1\,\Omega \]

This 1 \(\Omega\) is in series with the remaining 2 \(\Omega\) and 2 \(\Omega\) resistors:

\[ R_T = 2 + 1 + 2 = 5\,\Omega \]