A current of 5.0 A flows into the circuit in point- a and...

A current of $5.0$ A flows into the circuit in point- $a$ and out at point-b. (a) What is the potential difference from $a$ to b? (b) How much current flows through the $12.0-\Omega$ resistor? we found that the equivalent resistance for this combination is $11.6 \Omega$, and we are told the current through it is 5.0 A. (a) Voltage drop from $a$ to $b=I R_{\mathrm{eq}}=(5.0 \mathrm{~A})(11.6 \Omega)=58 \mathrm{~V}$ (b) The voltage drop from $a$ to $c$ is $(5.0 \mathrm{~A})(9.0 \Omega) 45 \mathrm{~V}$. Hence, from part $(a)$, the voltage drop from $c$ to $b$ is $$ 58 \mathrm{~V}-45 \mathrm{~V}=13 \mathrm{~V} $$ and the current in the $12.0-\Omega$ resistor is $$ I_{12}=\frac{V}{R}=\frac{13 \mathrm{~V}}{12 \Omega}=1.1 \mathrm{~A} $$

A current of $5.0$ A flows into the circuit in point- $a$ and out at point-b. (a) What is the potential difference from $a$ to b? (b) How much current flows through the $12.0-\Omega$ resistor?
we found that the equivalent resistance for this combination is $11.6 \Omega$, and we are told the current through it is 5.0 A.
(a) Voltage drop from $a$ to $b=I R_{\mathrm{eq}}=(5.0 \mathrm{~A})(11.6 \Omega)=58 \mathrm{~V}$
(b) The voltage drop from $a$ to $c$ is $(5.0 \mathrm{~A})(9.0 \Omega) 45 \mathrm{~V}$. Hence, from part $(a)$, the voltage drop from $c$ to $b$ is
$$
58 \mathrm{~V}-45 \mathrm{~V}=13 \mathrm{~V}
$$
and the current in the $12.0-\Omega$ resistor is
$$
I_{12}=\frac{V}{R}=\frac{13 \mathrm{~V}}{12 \Omega}=1.1 \mathrm{~A}
$$

Key Concepts

Ohm's Law

Ohm's Law is a fundamental principle in circuit analysis, stating that the voltage across a resistor is directly proportional to the current flowing through it, with the resistance acting as the proportionality constant. It is expressed mathematically as V = IR and is used to calculate voltage drops, current flows, and resistance values in electrical circuits.

Equivalent Resistance

Equivalent resistance represents a single resistor that can replace an entire network of series and parallel resistors without affecting the overall circuit behavior. Calculating the equivalent resistance simplifies the analysis of complex circuits by reducing them to simpler forms, allowing for easier calculation of current distribution and voltage drops.

Voltage Drop

Voltage drop refers to the loss of electrical potential as current flows through a resistor or circuit element. This concept is key in determining how the supplied voltage is distributed across various components in the circuit, which is critical for ensuring components operate within their designed voltage limits.

Current Division

Current division is the method used to determine how current splits among different parallel pathways in a circuit. It involves dividing the total current in inverse proportion to the resistances of the individual parallel branches, enabling precise calculation of current through each component.

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