Explanation

(a)G) Root-mean-square value of an alternating Current 1s the value of a.c. current that has the same heating effect as d.c. current.

(ii) Impedance is the effective resistance of an electric circuit arising from the combined effects of ohmic resistance, capacitance and inductive reactance.

(b) Current in circuit I = 60/120 = 0.5A

Voltage across device V\(_R\) = 120v

Voltage across capacitor = V\(_C\) = √[V\(^2\) - V\(_R\)\(^2\)]

V\(_C\)  = √[240\(^2\) - 120°]

V\(_C\) = 207.847v

I\(_C\) = I = 0.5A

X\(_C\) = V\(_C\) / I\(_C\)

= \(\frac{207.846}{0.5) → 415.7Ω

Capicitance, C = \(\frac{X_c}{2πf}\)

= \(\frac{415.7}{2 * 3.142 * 50}\)

= 1.323F

The capacitance C of a capacitor is the ratio of the amount of charge q on its plates to the potential difference between them, i.e C = q/v

(ii) I - charge on both capacitors are the same q1 = q2

Total capacitance, C = \(\frac{C_1 C_2}{C_1 + C_2}\)

C = \(\frac{C_2}{1 + C_1/C_2}\)  = \(\frac{C_2}{1 + V_1 + C_2}\)

C = \(\frac{C_2 V_2}{V_1 + C_2}\) = \(\frac{C_2 V_2}{2}\)

C = 1/2 = \(C_2 V_2\)

II - voltage across      V\(_1\) = \(\frac{C_2}{C_1 + C_2}\) * V

V\(_1\) = \(\frac{1}{C_1_{C_2} + 1}\) * V

but \(\frac{C_1}{C_2}\) = \(\frac{C_1}{C_2}\) = \(\frac{5}{2}\)

V\(_1\) = \(\frac{1}{5}{2} + 1}\) * 2

= \(\frac{2}{7}\) * 2 = \(\frac{4}{7}\) V

Voltage across C\(_2\) : V\(_2\) = 2 = \(\frac{4}{7}\) = \(\frac{10}{7}\) V 

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