Calculate the power used in the $2Ω$ resistor in each of the following circuits:

A $6V$ battery in series with $1Ω$ and $2Ω$ resistors.

A $4V$ battery in parallel with $12Ω$ and $2Ω$ resistors.

Q: Calculate the power used in the $2Ω$ resistor in each of the following circuits: 1. A $6V$ battery in series with $1Ω$ and $2Ω$ resistors. 2. A $4V$ battery in parallel with $12Ω$ and $2Ω$ resistors.

1. V = 6 Volt, R1 = $\text{R}_1=1\Omega,$ $\text{R}_2=2\Omega$ Equivalent resistance $=\text{R}_1+\text{R}_2=1+2=3\Omega$ Total current, $\text{I}=\frac{\text{V}}{\text{R}}=\frac{6}{3}=2\text{A}$ Current through $R_2 = I_2= I = 2A$ Voltage across $R_2 = V_2 = I_2R_2 = 2 \times 2 = 4$ Power used in $R_2 = I_2V_2= 2 \times 4 = 8W$ 2. V = 4Volt, $\text{R}_1=12\Omega$ $\text{R}_2=2\Omega$ Voltage across $R_2 = V_2 = V = 4V$ Current across $\text{R}_2=\text{I}_2=\frac{\text{V}_2}{\text{R}_2}=\frac{4}{2}=2\text{A}$ Poower used in $R_2 = I_2V_2 = 2 \times 4 = 8W$

Question

Calculate the power used in the $2Ω$ resistor in each of the following circuits:

A $6V$ battery in series with $1Ω$ and $2Ω$ resistors.
A $4V$ battery in parallel with $12Ω$ and $2Ω$ resistors.

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Solution

V = 6 Volt, R1 = $\text{R}_1=1\Omega,$ $\text{R}_2=2\Omega$

Equivalent resistance $=\text{R}_1+\text{R}_2=1+2=3\Omega$
Total current, $\text{I}=\frac{\text{V}}{\text{R}}=\frac{6}{3}=2\text{A}$
Current through $R_2 = I_2= I = 2A$
Voltage across $R_2 = V_2 = I_2R_2 = 2 \times 2 = 4$
Power used in $R_2 = I_2V_2= 2 \times 4 = 8W$

V = 4Volt, $\text{R}_1=12\Omega$ $\text{R}_2=2\Omega$

Voltage across $R_2 = V_2 = V = 4V$
Current across $\text{R}_2=\text{I}_2=\frac{\text{V}_2}{\text{R}_2}=\frac{4}{2}=2\text{A}$
Poower used in $R_2 = I_2V_2 = 2 \times 4 = 8W$

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