Problem: Consider the three circuits shown above. All the resistors and all the batteries are identical. (select true or false)a. The total power dissipated in circuit C is twice the total power dissipated in circuit B.b. The power dissipated in circuit A is twice the power dissipated in circuit B.c. The current through a resistor is the same in circuits A and C.d. The voltage across a single resistor in circuit C is twice the voltage across a single resistor in circuit B.e. The current through a resistor is the same in circuits A and B.

FREE Expert Solution

In this problem, we'll verify the statements by considering the following equations:

Power in circuits:

$\boxed{\mathbf{P}\mathbf{=}\mathbf{V}\mathbf{i}\mathbf{=}{\mathbf{i}}^{\mathbf{2}}\mathbf{R}\mathbf{=}\frac{{\mathbf{V}}^{\mathbf{2}}}{\mathbf{R}}}$

Ohm's law:

$\boxed{\mathit{i}\mathbf{=}\frac{\mathbf{V}}{\mathbf{R}}}$

Equivalent resistance for 2 resistors in parallel:

$\boxed{{\mathbf{R}}_{\mathbf{eq}}\mathbf{=}\frac{{\mathbf{R}}_{\mathbf{1}}{\mathbf{R}}_{\mathbf{2}}}{{\mathbf{R}}_{\mathbf{1}}\mathbf{+}{\mathbf{R}}_{\mathbf{2}}}}$

Equivalent resistance for resistors in series:

$\boxed{{\mathbf{R}}_{\mathbf{eq}}\mathbf{=}{\mathbf{R}}_{\mathbf{1}}\mathbf{+}{\mathbf{R}}_{\mathbf{2}}\mathbf{+}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{+}{\mathbf{R}}_{\mathbf{n}}}$

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