Power in Circuits Video Lessons

Concept

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:

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

Ohm's law:

$\overline{){\mathbit{i}}{\mathbf{=}}\frac{\mathbf{V}}{\mathbf{R}}}$

Equivalent resistance for 2 resistors in parallel:

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

Equivalent resistance for resistors in series:

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

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Problem Details

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.