Four resistors are connected to a battery with a terminal...

Four resistors are connected to a battery with a terminal voltage of $12.0 \mathrm{V},$ as shown below. Determine the following: a. the equivalent resistance for the circuit. b. the current in the battery. c. the current in the $30.0 \Omega$ resistor. d. the power dissipated by the $50.0 \Omega$ resistor. e. the power dissipated by the $20.0 \Omega$ resistor (Hint: Remember that $P=\frac{(\Delta V)^{2}}{R}=I \Delta V$.)

Four resistors are connected to a battery with a terminal voltage of $12.0 \mathrm{V},$ as shown below. Determine the following:
a. the equivalent resistance for the circuit.
b. the current in the battery.
c. the current in the $30.0 \Omega$ resistor.
d. the power dissipated by the $50.0 \Omega$ resistor.
e. the power dissipated by the $20.0 \Omega$ resistor (Hint: Remember that $P=\frac{(\Delta V)^{2}}{R}=I \Delta V$.)

Key Concepts

Electrical Power Dissipation

In circuits, power dissipation refers to the conversion of electrical energy into heat within resistive components. The power dissipated by a resistor can be calculated using formulas such as P = I^2R or P = V^2/R, enabling an understanding of how energy is used or lost in various parts of the circuit.

Equivalent Resistance

The concept of equivalent resistance allows a complex resistor network to be simplified into a single resistor that has the same effect on the circuit as the original network. Calculating the equivalent resistance is a key step in analyzing circuits, as it enables the use of Ohm’s Law to find the total current supplied by the battery.

Series and Parallel Resistor Combinations

Resistors in circuits can be arranged in series, where their resistances add directly, or in parallel, where the reciprocal of the equivalent resistance is the sum of the reciprocals of the individual resistances. Understanding these combinations is crucial to determining the overall resistance (or equivalent resistance) of a complex circuit.

Ohm's Law

This is the fundamental relationship in electrical circuits that relates voltage, current, and resistance by the equation V = IR. It is used to calculate any one of these quantities when the other two are known, and forms the basis for analyzing current flow and voltage drops in a circuit.

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