Resistor worksheet

1. Total resistance (parallel): 73.3 Ω

1. In parallel, every resistor gets the same voltage. So add the reciprocals: 1 divided by each value

   $\frac{1}{R}$$=\frac{1}{140}+\frac{1}{250}+\frac{1}{400}$$=0.0136428571\text{\hspace{0.17em}S}$

2. Turn that sum back into a resistance by taking 1 divided by it. This is the total

   $R$$=\frac{1}{0.0136428571}$$=73.2984293194\text{\hspace{0.17em}Ω}$

3. Find the total current I from the supply with Ohm's law: the voltage V divided by the total resistance R

   $I$$=\frac{10}{73.2984293194}$$=0.1364285714\text{\hspace{0.17em}A}$

4. Find the total power P: the voltage times the current

   $P$$=10\times 0.1364285714$$=1.3642857143\text{\hspace{0.17em}W}$

5. Each resistor gets the full supply voltage. So for the first one, R₁, divide the voltage by its resistance to get its current

   $\mathrm{I₁}$$=\frac{10}{140}$$=0.0714285714\text{\hspace{0.17em}A}$

6. Find the power (heat) in R₁: the voltage squared divided by its resistance

   $\mathrm{P₁}$$=\frac{{10}^2}{140}$$=0.7142857143\text{\hspace{0.17em}W}$

2. Total resistance (series): 790 Ω

1. In series, the same current passes through every resistor, so just add the resistances

   $R$$=100+220+470$$=790\text{\hspace{0.17em}Ω}$

2. Find the total current I from the supply with Ohm's law: the voltage V divided by the total resistance R

   $I$$=\frac{8}{790}$$=0.0101265823\text{\hspace{0.17em}A}$

3. Find the total power P: the voltage times the current

   $P$$=8\times 0.0101265823$$=0.0810126582\text{\hspace{0.17em}W}$

4. Each resistor takes a share of the voltage that matches its resistance. For the first one, R₁, multiply the current by its resistance

   $\mathrm{V₁}$$=0.0101265823\times 100$$=1.0126582278\text{\hspace{0.17em}V}$

5. Find the power (heat) in R₁: the current squared times its resistance

   $\mathrm{P₁}$$={0.0101265823}^2\times 100$$=0.0102547669\text{\hspace{0.17em}W}$

3. Total resistance (parallel): 59.98 Ω

1. In parallel, every resistor gets the same voltage. So add the reciprocals: 1 divided by each value

   $\frac{1}{R}$$=\frac{1}{100}+\frac{1}{220}+\frac{1}{470}$$=0.0166731141\text{\hspace{0.17em}S}$

2. Turn that sum back into a resistance by taking 1 divided by it. This is the total

   $R$$=\frac{1}{0.0166731141}$$=59.9767981439\text{\hspace{0.17em}Ω}$

3. Find the total current I from the supply with Ohm's law: the voltage V divided by the total resistance R

   $I$$=\frac{11}{59.9767981439}$$=0.1834042553\text{\hspace{0.17em}A}$

4. Find the total power P: the voltage times the current

   $P$$=11\times 0.1834042553$$=2.0174468085\text{\hspace{0.17em}W}$

5. Each resistor gets the full supply voltage. So for the first one, R₁, divide the voltage by its resistance to get its current

   $\mathrm{I₁}$$=\frac{11}{100}$$=0.11\text{\hspace{0.17em}A}$

6. Find the power (heat) in R₁: the voltage squared divided by its resistance

   $\mathrm{P₁}$$=\frac{{11}^2}{100}$$=1.21\text{\hspace{0.17em}W}$

4. Total resistance (parallel): 61.49 Ω

1. In parallel, every resistor gets the same voltage. So add the reciprocals: 1 divided by each value

   $\frac{1}{R}$$=\frac{1}{120}+\frac{1}{190}+\frac{1}{375}$$=0.0162631579\text{\hspace{0.17em}S}$

2. Turn that sum back into a resistance by taking 1 divided by it. This is the total

   $R$$=\frac{1}{0.0162631579}$$=61.4886731392\text{\hspace{0.17em}Ω}$

3. Find the total current I from the supply with Ohm's law: the voltage V divided by the total resistance R

   $I$$=\frac{10}{61.4886731392}$$=0.1626315789\text{\hspace{0.17em}A}$

4. Find the total power P: the voltage times the current

   $P$$=10\times 0.1626315789$$=1.6263157895\text{\hspace{0.17em}W}$

5. Each resistor gets the full supply voltage. So for the first one, R₁, divide the voltage by its resistance to get its current

   $\mathrm{I₁}$$=\frac{10}{120}$$=0.0833333333\text{\hspace{0.17em}A}$

6. Find the power (heat) in R₁: the voltage squared divided by its resistance

   $\mathrm{P₁}$$=\frac{{10}^2}{120}$$=0.8333333333\text{\hspace{0.17em}W}$

5. Total resistance (parallel): 59.98 Ω

1. In parallel, every resistor gets the same voltage. So add the reciprocals: 1 divided by each value

   $\frac{1}{R}$$=\frac{1}{100}+\frac{1}{220}+\frac{1}{470}$$=0.0166731141\text{\hspace{0.17em}S}$

2. Turn that sum back into a resistance by taking 1 divided by it. This is the total

   $R$$=\frac{1}{0.0166731141}$$=59.9767981439\text{\hspace{0.17em}Ω}$

3. Find the total current I from the supply with Ohm's law: the voltage V divided by the total resistance R

   $I$$=\frac{14}{59.9767981439}$$=0.2334235977\text{\hspace{0.17em}A}$

4. Find the total power P: the voltage times the current

   $P$$=14\times 0.2334235977$$=3.2679303675\text{\hspace{0.17em}W}$

5. Each resistor gets the full supply voltage. So for the first one, R₁, divide the voltage by its resistance to get its current

   $\mathrm{I₁}$$=\frac{14}{100}$$=0.14\text{\hspace{0.17em}A}$

6. Find the power (heat) in R₁: the voltage squared divided by its resistance

   $\mathrm{P₁}$$=\frac{{14}^2}{100}$$=1.96\text{\hspace{0.17em}W}$

6. Total resistance (series): 970 Ω

1. In series, the same current passes through every resistor, so just add the resistances

   $R$$=140+255+575$$=970\text{\hspace{0.17em}Ω}$

2. Find the total current I from the supply with Ohm's law: the voltage V divided by the total resistance R

   $I$$=\frac{13}{970}$$=0.0134020619\text{\hspace{0.17em}A}$

3. Find the total power P: the voltage times the current

   $P$$=13\times 0.0134020619$$=0.1742268041\text{\hspace{0.17em}W}$

4. Each resistor takes a share of the voltage that matches its resistance. For the first one, R₁, multiply the current by its resistance

   $\mathrm{V₁}$$=0.0134020619\times 140$$=1.8762886598\text{\hspace{0.17em}V}$

5. Find the power (heat) in R₁: the current squared times its resistance

   $\mathrm{P₁}$$={0.0134020619}^2\times 140$$=0.0251461367\text{\hspace{0.17em}W}$

7. Total resistance (parallel): 59.64 Ω

1. In parallel, every resistor gets the same voltage. So add the reciprocals: 1 divided by each value

   $\frac{1}{R}$$=\frac{1}{100}+\frac{1}{220}+\frac{1}{450}$$=0.0167676768\text{\hspace{0.17em}S}$

2. Turn that sum back into a resistance by taking 1 divided by it. This is the total

   $R$$=\frac{1}{0.0167676768}$$=59.6385542169\text{\hspace{0.17em}Ω}$

3. Find the total current I from the supply with Ohm's law: the voltage V divided by the total resistance R

   $I$$=\frac{9}{59.6385542169}$$=0.1509090909\text{\hspace{0.17em}A}$

4. Find the total power P: the voltage times the current

   $P$$=9\times 0.1509090909$$=1.3581818182\text{\hspace{0.17em}W}$

5. Each resistor gets the full supply voltage. So for the first one, R₁, divide the voltage by its resistance to get its current

   $\mathrm{I₁}$$=\frac{9}{100}$$=0.09\text{\hspace{0.17em}A}$

6. Find the power (heat) in R₁: the voltage squared divided by its resistance

   $\mathrm{P₁}$$=\frac{9^2}{100}$$=0.81\text{\hspace{0.17em}W}$

8. Total resistance (series): 675 Ω

1. In series, the same current passes through every resistor, so just add the resistances

   $R$$=100+150+425$$=675\text{\hspace{0.17em}Ω}$

2. Find the total current I from the supply with Ohm's law: the voltage V divided by the total resistance R

   $I$$=\frac{11}{675}$$=0.0162962963\text{\hspace{0.17em}A}$

3. Find the total power P: the voltage times the current

   $P$$=11\times 0.0162962963$$=0.1792592593\text{\hspace{0.17em}W}$

4. Each resistor takes a share of the voltage that matches its resistance. For the first one, R₁, multiply the current by its resistance

   $\mathrm{V₁}$$=0.0162962963\times 100$$=1.6296296296\text{\hspace{0.17em}V}$

5. Find the power (heat) in R₁: the current squared times its resistance

   $\mathrm{P₁}$$={0.0162962963}^2\times 100$$=0.0265569273\text{\hspace{0.17em}W}$

9. Total resistance (parallel): 59.98 Ω

1. In parallel, every resistor gets the same voltage. So add the reciprocals: 1 divided by each value

   $\frac{1}{R}$$=\frac{1}{100}+\frac{1}{220}+\frac{1}{470}$$=0.0166731141\text{\hspace{0.17em}S}$

2. Turn that sum back into a resistance by taking 1 divided by it. This is the total

   $R$$=\frac{1}{0.0166731141}$$=59.9767981439\text{\hspace{0.17em}Ω}$

3. Find the total current I from the supply with Ohm's law: the voltage V divided by the total resistance R

   $I$$=\frac{7}{59.9767981439}$$=0.1167117988\text{\hspace{0.17em}A}$

4. Find the total power P: the voltage times the current

   $P$$=7\times 0.1167117988$$=0.8169825919\text{\hspace{0.17em}W}$

5. Each resistor gets the full supply voltage. So for the first one, R₁, divide the voltage by its resistance to get its current

   $\mathrm{I₁}$$=\frac{7}{100}$$=0.07\text{\hspace{0.17em}A}$

6. Find the power (heat) in R₁: the voltage squared divided by its resistance

   $\mathrm{P₁}$$=\frac{7^2}{100}$$=0.49\text{\hspace{0.17em}W}$

10. Total resistance (series): 790 Ω

1. In series, the same current passes through every resistor, so just add the resistances

   $R$$=100+220+470$$=790\text{\hspace{0.17em}Ω}$

2. Find the total current I from the supply with Ohm's law: the voltage V divided by the total resistance R

   $I$$=\frac{11}{790}$$=0.0139240506\text{\hspace{0.17em}A}$

3. Find the total power P: the voltage times the current

   $P$$=11\times 0.0139240506$$=0.153164557\text{\hspace{0.17em}W}$

4. Each resistor takes a share of the voltage that matches its resistance. For the first one, R₁, multiply the current by its resistance

   $\mathrm{V₁}$$=0.0139240506\times 100$$=1.3924050633\text{\hspace{0.17em}V}$

5. Find the power (heat) in R₁: the current squared times its resistance

   $\mathrm{P₁}$$={0.0139240506}^2\times 100$$=0.0193879186\text{\hspace{0.17em}W}$