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Q54PE

Expert-verifiedFound in: Page 777

Book edition
1st Edition

Author(s)
Paul Peter Urone

Pages
1272 pages

ISBN
9781938168000

**A ${\mathbf{0}}{\mathbf{.}}{\mathbf{0200}}{\mathbf{}}{\mathbf{\Omega}}$**** ammeter is placed in series with a ${\mathbf{10}}{\mathbf{.}}{\mathbf{00}}{\mathbf{\u2010}}{\mathbf{\Omega}}$**** resistor in a circuit. (a) Draw a circuit diagram of the connection. (b) Calculate the resistance of the combination. (c) If the voltage is kept the same across the combination as it was through the ${\mathbf{10}}{\mathbf{.}}{\mathbf{00}}{\mathbf{\u2010}}{\mathbf{\Omega}}$**** resistor alone, what is the percent decrease in current? (d) If the current is kept the same through the combination as it was through the ${\mathbf{10}}{\mathbf{.}}{\mathbf{00}}{\mathbf{\u2010}}{\mathbf{\Omega}}$**** resistor alone, what is the percent increase in voltage? (e) Are the changes found in parts (c) and (d) significant? Discuss.**

(a) The circuit diagram for the series connection of the ammeter in a resistor circuit is,

(b) The total resistance of the combination is ${\mathrm{R}}_{\mathrm{tot}}=10.02\mathrm{\Omega}$ .

(c) Percentage decrease in the current for the same voltage is role="math" localid="1656396884713" $0.1996\%$.

(d) If the current of the combinate is the same the increase in the voltage is $0.2\%$

(e) Since the results of current and voltage are very small, they are insignificant.

**The rate of electron flow can be described as the aggregate flow of electrons via a wire. The term "resistance" refers to anything that stands in the way of current flow. To convert electrical energy to light, heat, or movement, an electrical circuit must have resistance.**

**(a)**

The circuit diagram of the connection of an ammeter when a $0.02\mathrm{\Omega}$ ammeter is placed in series with a $10\mathrm{\Omega}$ resistor in a circuit is given below,

Therefore, the circuit diagram is obtained.

**(b)**

A $0.02\mathrm{\Omega}$ ammeter is placed in series with a $10\mathrm{\Omega}$ resistor in a circuit.

The formula for total resistance is,

${\mathrm{R}}_{\mathrm{combination}}=\mathrm{R}+\mathrm{r}\phantom{\rule{0ex}{0ex}}=10\mathrm{\Omega}+0.02\mathrm{\Omega}\phantom{\rule{0ex}{0ex}}=10.02\mathrm{\Omega}$

Therefore, the value for total resistance is ${\mathrm{R}}_{\mathrm{combination}}=10.02\mathrm{\Omega}$ .

**(c)**

Current through the only resistor is,

$\mathrm{I}=\frac{\mathrm{V}}{\mathrm{R}}\phantom{\rule{0ex}{0ex}}=\frac{\mathrm{V}}{10\mathrm{\Omega}}$

And current through combination is,

${\mathrm{I}}_{\mathrm{combination}}=\frac{\mathrm{V}}{{\mathrm{R}}_{\mathrm{combination}}}\phantom{\rule{0ex}{0ex}}=\frac{\mathrm{V}}{10.02\mathrm{\Omega}}$

The decrease in current is,

${\mathrm{P}}_{\mathrm{d}}=\left(\frac{{\mathrm{I}}_{\mathrm{combination}}-\mathrm{I}}{\mathrm{I}}\right)\times 100\%\phantom{\rule{0ex}{0ex}}=\left(\frac{\left(\frac{\mathrm{V}}{10.02\mathrm{\Omega}}\right)-\left(\frac{\mathrm{V}}{10\mathrm{\Omega}}\right)}{\left(\frac{\mathrm{V}}{10\mathrm{\Omega}}\right)}\right)\times 100\%\phantom{\rule{0ex}{0ex}}=-0.1996\%$

Therefore, the decrease in current is $0.1996\%$.

**(d)**

Voltage through the only resistor is,

$\mathrm{V}=\mathrm{IR}\phantom{\rule{0ex}{0ex}}=\mathrm{I}\times 10\mathrm{\Omega}$

And voltage through combination is,

${\mathrm{V}}_{\mathrm{Combination}}={\mathrm{IR}}_{\mathrm{Combination}}\phantom{\rule{0ex}{0ex}}=\mathrm{I}\times 10.02\mathrm{\Omega}$

The increase in voltage is,

${\mathrm{P}}_{\mathrm{I}}=\left(\frac{{\mathrm{V}}_{\mathrm{Combination}}-\mathrm{V}}{\mathrm{V}}\right)\times 100\%\phantom{\rule{0ex}{0ex}}=\left(\frac{\left(\mathrm{I}\times 10.02\mathrm{\Omega}\right)-\left(\mathrm{I}\times 10\mathrm{\Omega}\right)}{\left(\mathrm{I}\times 10\mathrm{\Omega}\right)}\right)\times 100\%\phantom{\rule{0ex}{0ex}}=0.2\%$

Therefore, the increase in voltage is $0.2\%$ .

**(e)**

The result for the decrease in current is $0.1996\%$ .

The result ofthe increase in voltage is $0.2\%$ .

These are very small amounts, so they do not affect the circuit in anyway.

Therefore, the results are not significant.

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