Question

voltage, current and resistance worksheet
resistance = potential difference / current
r = v / i
units: r is measured in ohms (ω)
v is measured in volts (v)
i is measured in amperes (a)

1. solve for the unknown measurement.

a) i = 10 a
r = 1500 ω
v = ?
b) i = ?
r = 200 ω
v = 240 v
c) i = 15 a
r = ?
v = 110 v

1. find the unknown quantity (convert to the base unit first, then solve).

a) i = ?
r = 20 ω
v = 350 mv = ______ v
b) r = ?
i = 25 ma = ______ a
v = 110 v
c) i = 15 a
r = 7333 mω = ______ ω
v = ?
word problems — be sure to check your units before solving the following questions!

1. how much resistance does a light bulb create if it has a current of 25 ma around it in a 9 v circuit?

i = 25 ma =
v =
r = ?

1. how much current flows through a 16 v battery that has a resistance of 5.1 ω?
2. the human body offers a very small amount of resistance (let’s say 1 mω for argument). if a lightning bolt (said to have 1.21 gv of potential according to a famous movie called back to the future released in 1984) hits you, how much current is flowing through your body? ps. it takes a mere 50 ma of current to kill a human being.

Explanation:

1. Solve for the unknown measurement

Part a: Solve for V

Rearrange $R=\frac{V}{I}$ to $V=R \times I$
$V = 1500\ \Omega \times 10\ \text{A} = 15000\ \text{V}$

Part b: Solve for I

Rearrange $R=\frac{V}{I}$ to $I=\frac{V}{R}$
$I = \frac{240\ \text{V}}{200\ \Omega} = 1.2\ \text{A}$

Part c: Solve for R

Use $R=\frac{V}{I}$
$R = \frac{110\ \text{V}}{15\ \text{A}} \approx 7.33\ \Omega$

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2. Convert units first, then solve

Part a: Convert V, solve for I

Convert $350\ \text{mV}$ to V: $350\ \text{mV} = 0.35\ \text{V}$
Use $I=\frac{V}{R}$
$I = \frac{0.35\ \text{V}}{20\ \Omega} = 0.0175\ \text{A}$

Part b: Convert I, solve for R

Convert $25\ \text{mA}$ to A: $25\ \text{mA} = 0.025\ \text{A}$
Use $R=\frac{V}{I}$
$R = \frac{110\ \text{V}}{0.025\ \text{A}} = 4400\ \Omega$

Part c: Convert R, solve for V

Convert $7333\ \text{m}\Omega$ to $\Omega$: $7333\ \text{m}\Omega = 7.333\ \Omega$
Use $V=R \times I$
$V = 7.333\ \Omega \times 15\ \text{A} = 109.995\ \text{V} \approx 110\ \text{V}$

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3. Light bulb resistance problem

Convert $25\ \text{mA}$ to A: $25\ \text{mA} = 0.025\ \text{A}$, $V=9\ \text{V}$
Use $R=\frac{V}{I}$
$R = \frac{9\ \text{V}}{0.025\ \text{A}} = 360\ \Omega$

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4. Battery current problem

Use $I=\frac{V}{R}$
$I = \frac{16\ \text{V}}{5.1\ \Omega} \approx 3.14\ \text{A}$

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5. Lightning current problem

Convert units: $1\ \text{m}\Omega = 0.001\ \Omega$, $1.21\ \text{GV} = 1.21 \times 10^9\ \text{V}$
Use $I=\frac{V}{R}$
$I = \frac{1.21 \times 10^9\ \text{V}}{0.001\ \Omega} = 1.21 \times 10^{12}\ \text{A}$

Answer:

1.
a) $15000\ \text{V}$
b) $1.2\ \text{A}$
c) $\approx 7.33\ \Omega$

2.
a) $0.35\ \text{V}$, $0.0175\ \text{A}$
b) $0.025\ \text{A}$, $4400\ \Omega$
c) $7.333\ \Omega$, $\approx 110\ \text{V}$

3.
$I=0.025\ \text{A}$, $V=9\ \text{V}$, $R=360\ \Omega$

4.
$\approx 3.14\ \text{A}$

5.
$1.21 \times 10^{12}\ \text{A}$