Question

Physics E&M

Posted about 1 month ago

```
17 Several e.m.f.s, resistors and a switch, $S$, are connected as shown in the circuit diagram below.
$I_{1}, I_{2}$ and $I_{3}$ show the current flow in the circuit. Determine the value of $I_{2}$
(a) when $S$ is opened
[4]
(b) when $S$ is closed
$[3]$
18 (a) Three identical capacitors are connected to an e.m.f., $E$, as shown in the circuit diagram below.
(i) Derive an expression for the effective capacitance in terms of $C$.
[3]
(ii) Determine the total energy stored in terms of $C$ and $E$.
[2]
(b) A fully charged parallel plate capacitor of capacitance $100 \mu \mathrm{F}$, a variable resistor, $R$, and 'a switch, $S$, are connected as shown in the circuit diagram below.
(i) When $S$ is closed, the charge reduces to half in time of 3.0 ms . Determine the resistance of $R$.
[4]
(ii) If a material of dielectric constant 4.2 is inserted in between the plates, determine the time constant.
[2]
(c) Describe the effect of dielectric on the capacitance when a capacitor is connected to a potential difference.
$[4]$
```

Sign in to unlock the answer

Answer from Sia

Posted about 1 month ago

```
Sure, let's break down the questions one by one.
Question 1:
Determine the value of $I_{2}$:
(a) when $S$ is opened
(b) when $S$ is closed
# Answer:
For part (a):
```

D

```
For part (b):
```

D

```
# Explanation:
```

Key Concept

Kirchhoff's Voltage Law (KVL)

Explanation

When the switch $S$ is open, the circuit is divided into separate loops, and we can apply KVL to each loop to find the current $I_2$. When the switch $S$ is closed, the circuit forms a single loop, and we again use KVL to find the new value of $I_2$.

```
Question 2:
(a) Three identical capacitors are connected to an e.m.f., $E$:
(i) Derive an expression for the effective capacitance in terms of $C$.
(ii) Determine the total energy stored in terms of $C$ and $E$.
# Answer:
For part (i):
```

D

```
For part (ii):
```

D

```
# Explanation:
```

Key Concept

Capacitors in Parallel

Explanation

When capacitors are connected in parallel, the total capacitance $C_{total}$ is the sum of the individual capacitances: $C_{total} = C + C + C = 3C$. The energy stored in a capacitor is given by $U = \frac{1}{2} C V^2$. For three capacitors in parallel, the total energy stored is $U_{total} = \frac{1}{2} (3C) E^2$.

```
Question 3:
(b) A fully charged parallel plate capacitor of capacitance $100 \mu \mathrm{F}$, a variable resistor, $R$, and a switch, $S$:
(i) When $S$ is closed, the charge reduces to half in time of 3.0 ms. Determine the resistance of $R$.
(ii) If a material of dielectric constant 4.2 is inserted in between the plates, determine the time constant.
# Answer:
For part (i):
```

D

```
For part (ii):
```

D

```
# Explanation:
```

Key Concept

RC Time Constant

Explanation

The time constant $\tau$ for an RC circuit is given by $\tau = RC$. When the charge reduces to half, the time $t = \tau \ln(2)$. Given $t = 3.0$ ms, we can solve for $R$. For part (ii), inserting a dielectric increases the capacitance by a factor of the dielectric constant, so the new time constant is $\tau' = R \cdot (4.2 \cdot 100 \mu \mathrm{F})$.

```
Question 4:
(c) Describe the effect of dielectric on the capacitance when a capacitor is connected to a potential difference.
# Answer:
```

D

```
# Explanation:
```

Key Concept

Dielectric Effect

Explanation

A dielectric material increases the capacitance of a capacitor by reducing the electric field within the capacitor for a given charge on the plates. This is quantified by the dielectric constant $k$, where the new capacitance $C' = kC$.

Not the question you are looking for? Ask here!

Enter question by text

Enter question by image

Upgrade to Asksia Pro

Join a AskSia's Pro Plan, and get 24/7 AI tutoring for your reviews, assignments, quizzes and exam preps.

Unlimited chat query usages

Strong algorithms that better know you

Early access to new release features

Study Other Question