Analysis, Conclusions and Evaluation

Connect the 100 $\Omega$ resistor between points A and B in the circuit.

(i) Using two connecting leads, connect the voltmeter between points A and C. Close the switch and measure the potential difference $V_{AC}$.

$V_{AC}$ = ______

(ii) Open the switch and disconnect the voltmeter. Connect the voltmeter between points B and C. Close the switch and measure the potential difference $V_{BC}$.
Open the switch.

$V_{BC}$ = ______

(iii) Calculate the ratio $F_1$ of the potential differences using

$F_1$ = ______

Replace the 100 $\Omega$ resistor with the 220 $\Omega$ resistor. Repeat (a)(i) and (a)(ii) to obtain new values for $V_{AC}$ and $V_{BC}$.

Calculate a new value $F_2$ for the ratio of the potential differences.

$V_{AC}$ = ______
$V_{BC}$ = ______
$F_2$ = ______

Using ideas about potential dividers, explain why $V_{BC}$ has changed.

Connect the 100 $\Omega$ resistor between points A and B in the circuit.

(i) Using two connecting leads, connect the voltmeter between points A and C. Close the switch and measure the potential difference $V_{AC}$.

$V_{AC}$ = ______

(ii) Open the switch and disconnect the voltmeter. Connect the voltmeter between points B and C. Close the switch and measure the potential difference $V_{BC}$.
Open the switch.

$V_{BC}$ = ______

(iii) Calculate the ratio $F_1$ of the potential differences using

$F_1$ = ______

Replace the 100 $\Omega$ resistor with the 220 $\Omega$ resistor. Repeat (a)(i) and (a)(ii) to obtain new values for $V_{AC}$ and $V_{BC}$.

Calculate a new value $F_2$ for the ratio of the potential differences.

$V_{AC}$ = ______
$V_{BC}$ = ______
$F_2$ = ______

Using ideas about potential dividers, explain why $V_{BC}$ has changed.

Calculate the flow rate $F$ using the equation

where $V = 30\ \text{cm}^3$. Give the unit of your answer.

$F$ = ______ unit ______

(iv) Empty the water from the measuring cylinder back into the beaker.

Repeat (a)(i) and as you pour the water into the can, start the stopwatch.

Measure the time $t$ when there is 60 $\text{cm}^3$ of water in the measuring cylinder.

$t$ = ______ $\text{s}$

(v) Calculate the flow rate $F$ for $V = 60\ \text{cm}^3$. Give the unit of your answer.

$F$ = ______ unit ______

Empty the water from the measuring cylinder back into the beaker.

Continue the investigation.

Pour 150 $\text{cm}^3$ of water from the beaker into the can and record the readings on the stopwatch when the volume of the water in the measuring cylinder reaches values in the range 30 $\text{cm}^3$ to 100 $\text{cm}^3$.

• Record all of your results in the table of Fig. 4.2.
• Repeat the experiment once and calculate the average times.
• Write headings in the top row of the results table of Fig. 4.2.

(Do not calculate the flow rates)

Fig. 4.2

On the grid opposite, plot a graph of time on the $y$-axis against volume on the $x$-axis.

Draw the curve of best fit through your points.

Draw a tangent to the curve when the volume of water is 70 $\text{cm}^3$.

Determine the gradient $G$ of the tangent at this point.

$G$ = ______

Use the equation $M_B = 5d_0$ to calculate the mass $M_B$ of the $250\text{ cm}^3$ beaker.

$M_B$ = ______ $\text{g}$

Use the measuring cylinder to pour a volume $V$ of $30\text{ cm}^3$ of cooking oil into the beaker. Record the volume that you have added in the first column of the results table of Fig. 4.2.

Rebalance the beam by moving the $200\text{ g}$ mass.

Measure the horizontal distance $d$ from the $200\text{ g}$ mass to the pivot.

$d$ = ______ $\text{cm}$

Record $d$ in the second column in Fig. 4.2.

Use your answer to (b) and the equation

to calculate the mass $M$ of $30\text{ cm}^3$ of oil. Record $M$ in the third column of the results table.

$M$ = ______ $\text{g}$

Table of Fig. 4.2:

Fig. 4.2

(i) Continue to add approximately $30\text{ cm}^3$ of oil at a time until there is a total of $150\text{ cm}^3$ of oil in the beaker.

Record the total volume $V$ of oil in the first column of Fig. 4.2.

(ii) Rebalance the beam each time you add some oil by moving the $200\text{ g}$ mass.

Record the corresponding values of $d$ in Fig. 4.2.

(iii) Use the equation in (c) to calculate the mass $M$ of the volume of the oil in the beaker.

Record your answers in the third column of Fig. 4.2.

(iv) Write headings in the top row of the results table of Fig. 4.2.

On the grid opposite, plot a graph of $M$ on the $y$-axis against $V$ on the $x$-axis.

Draw the straight line of best fit.

Determine the gradient $G$ of your graph.

$G$ = ______

The equation used to calculate the density $\rho$ of a substance is

State the relationship between the gradient of your graph and the density of the oil.

Open the switch. Connect the resistor of resistance $R = 10\ \Omega$ between points A and B.

(i) Close the switch and record the reading $V$ on the voltmeter.

$V$ = ______

(ii) Open the switch. Calculate the current $I$ in the circuit using

$I$ = ______

Each time you take a reading on the voltmeter, close the switch and open it after you have taken your reading.

Fig. 4.2

(i) Fig. 4.2 is a table for your results and calculations. Add units to the headings in the table. Transfer your values for $R$, $V$ and $I$ from (b) into the table.

(ii) Remove the $10\ \Omega$ resistor from the circuit and replace it with the $22\ \Omega$ resistor. Record the new reading $V$ in Fig. 4.2. Calculate the new current $I$ in the circuit and record it in Fig. 4.2 along with the resistance $R$ used.

(iii) Replace the $22\ \Omega$ resistor with the $39\ \Omega$ resistor and obtain new values for $V$ and $I$. Record these in Fig. 4.2 along with the resistance $R$ used.

(iv) Remove the $39\ \Omega$ resistor.

For two resistors in series $R_{\text{total}} = R_1 + R_2$.

Calculate three possible values of resistance that can be obtained by connecting the $10\ \Omega$, the $22\ \Omega$ and the $39\ \Omega$ resistors in series. Record these values in Fig. 4.2. For each of your values, obtain values for $V$ and $I$ and record these in Fig. 4.2.

(v) For two resistors in parallel

Calculate the resistance of the $10\ \Omega$ and $22\ \Omega$ resistors when they are connected in parallel and record your value in Fig. 4.2. For this parallel combination, obtain values of $V$ and $I$ and record your values in Fig. 4.2.

Using the grid opposite, plot a graph of $V$ on the $y$-axis against $I$ on the $x$-axis. Start your axes at the origin. Draw a straight line of best fit.

Determine the gradient $G$ of the line of best fit. Show your working.

$G$ = ______

Use your graph to find the value of $V$ at $I = 0$.

$V$ = ______