Alternating Currents

State the type of rectification produced by the circuit of Fig. 8.1.

Calculate $V_0$.

$V_0$ = ______ $\text{V}$

Determine the peak power $P_0$ in the resistor.

$P_0$ = ______ $\text{W}$

On Fig. 8.3, sketch the variation of the power $P$ in the resistor with $t$ between $t = 0$ and $t = 2T$.

Use the answer in (b)(ii) to explain why the mean power in the resistor is $\frac{1}{4}P_0$.

Use the information in (b)(iii) to determine the r.m.s. value of $V_{OUT}$.

r.m.s. voltage = ______ $\text{V}$

Complete Fig. 8.1 for the bridge rectifier such that the point A is at a positive potential with respect to point B.

On Fig. 8.2, draw a line to show the variation of the potential difference $V$ across the load resistor with time $t$. Your line should extend from $t = 0.5T$ to $t = 2.0T$.

Use your line in (b)(i) to determine, in terms of $T$, the time constant of the smoothing circuit.

time constant = ______ $T$

The resistance of the load resistor is now increased. The capacitance of the capacitor is unchanged.

State and explain the effect of this change on the smoothed output p.d.

show that the period is $0.050\text{ s}$

determine the root-mean-square (r.m.s.) voltage.

$\text{r.m.s. voltage}$ = ______ $\text{V}$

On Fig. 7.1, sketch the variation of $V$ with $t$ for values of $t$ from $t = 0$ to $t = 100\text{ ms}$.

The alternating voltage is rectified to produce an output voltage across a load resistor R, as shown in Fig. 7.2.

Fig. 7.3 shows the variation with $t$ of the power $P$ in the load resistor.

State three conclusions that can be drawn from Fig. 7.3. The conclusions may be qualitative or quantitative. Use the space for any working.

State the purpose of the circuit in Fig. 7.1.

The load resistor $R$ has a resistance of $370\ \Omega$.

Show that the maximum power dissipated in $R$ is $0.22\ \text{W}$.

On Fig. 7.3, sketch the variation with $t$ of the power $P$ dissipated in $R$.

Calculate the mean power dissipated in $R$.

mean power = ______ $\text{W}$

The circuit of Fig. 7.1 is disconnected, and $R$ is connected directly across the power supply.

Explain, without calculation, how the mean power now dissipated in $R$ compares with the answer in (b)(iii).

State the purpose of the circuit in Fig. 7.1.

The load resistor $R$ has a resistance of $370\ \Omega$.

Show that the maximum power dissipated in $R$ is $0.22\ \text{W}$.

On Fig. 7.3, sketch the variation with $t$ of the power $P$ dissipated in $R$.

Calculate the mean power dissipated in $R$.

mean power = ______ $\text{W}$

The circuit of Fig. 7.1 is disconnected, and $R$ is connected directly across the power supply.

Explain, without calculation, how the mean power now dissipated in $R$ compares with the answer in (b)(iii).

State what is meant by rectification of an alternating voltage.

State the difference between half-wave rectification and full-wave rectification.

Complete Fig. 6.1 to show a circuit that produces half-wave rectification of an alternating input voltage $V_{IN}$ to produce output voltage $V_{OUT}$ across the resistor $R$.

State the purpose of the capacitor $C$ in the circuit of Fig. 6.1.

Show that the capacitance of $C$ is $570\ \mu\text{F}$.

Determine the resistance of $R$.

resistance = ______ $\Omega$

State what is meant by the frequency of an alternating current.

Show that the period of the alternating current is $50\text{ ms}$.

On Fig. 8.1, sketch the variation of $I$ with $t$ between $t = 0$ and $t = 100\text{ ms}$.

Determine the root-mean-square (r.m.s.) current in the resistor.

r.m.s. current = ______ $\text{A}$

Use data from (b), including your answer in (b)(iii), to show by calculation that the mean power in the $680\ \Omega$ resistor is half of the peak power.

State the name of the type of rectification produced by a bridge rectifier.

Complete Fig. 7.1 by drawing the three missing diodes, correctly connected.

On Fig. 7.1, draw an arrow to indicate the direction of the current in resistor $R$.

On Fig. 7.3, sketch the variation of $V_{OUT}$ with $t$ between $t = 0$ and $t = 2.0T$.

The power dissipated in the resistor is $P$.

On Fig. 7.4, sketch the variation of $P$ with $t$ between $t = 0$ and $t = 2.0T$.

Suggest, with a reason, how the root-mean-square (r.m.s.) value of $V_{OUT}$ compares with the r.m.s. value of $V_{IN}$.

the current is in the negative direction

$P$ = ______

the current is in the positive direction.

$P$ = ______

On Fig. 7.3, sketch the variation of $P$ with $t$ between $t = 0$ and $t = 2.0T$. Label the power axis with an appropriate scale.

the mean power $\langle P \rangle$ in the resistor

$\langle P \rangle$ = ______

the root-mean-square (r.m.s.) current $I_{\text{r.m.s.}}$ in the resistor.

$I_{\text{r.m.s.}}$ = ______

the current is in the negative direction

$P$ = ______

the current is in the positive direction.

$P$ = ______

On Fig. 7.3, sketch the variation of $P$ with $t$ between $t = 0$ and $t = 2.0T$. Label the power axis with an appropriate scale.

the mean power $\langle P \rangle$ in the resistor

$\langle P \rangle$ = ______

the root-mean-square (r.m.s.) current $I_{\text{r.m.s.}}$ in the resistor.

$I_{\text{r.m.s.}}$ = ______