What resistance must be placed in parallel with 12 Ωto...

Name: Problem 4, Chapter 28: Schaum’s Outline of College Physics
Uploaded: 2022-02-28T14:45:50-08:00
Duration: 41 s
Channel: Khoobchandra Agrawal
Description: What resistance must be placed in parallel with 12 Ωto obtain a combined resistance of 4 Ω? From (1)/(Req) =(1)/(R1)+(1)/(R2) we have (1)/(4 Ω) =(1)/(12 Ω)+(1)/(R2) and so R2=6 Ω

What resistance must be placed in parallel with $12 \Omega$ to obtain a combined resistance of $4 \Omega$ ? $$ \begin{array}{lc} \text { From } & \frac{1}{R_{\mathrm{eq}}} & =\frac{1}{R_{1}}+\frac{1}{R_{2}} \\ \text { we have } & \frac{1}{4 \Omega} & =\frac{1}{12 \Omega}+\frac{1}{R_{2}} \\ \text { and so } & R_{2}=6 \Omega \end{array} $$

What resistance must be placed in parallel with $12 \Omega$ to obtain a combined resistance of $4 \Omega$ ?
$$
\begin{array}{lc}
\text { From } & \frac{1}{R_{\mathrm{eq}}} & =\frac{1}{R_{1}}+\frac{1}{R_{2}} \\
\text { we have } & \frac{1}{4 \Omega} & =\frac{1}{12 \Omega}+\frac{1}{R_{2}} \\
\text { and so } & R_{2}=6 \Omega
\end{array}
$$

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Key Concepts

Parallel Resistive Networks

This concept involves connecting resistors such that the ends of each resistor are connected to the same two nodes. In such networks, the overall or equivalent resistance is always lower than the smallest individual resistor, as the circuit provides multiple paths for the current to travel.

Reciprocal Formula for Equivalent Resistance

In parallel circuits, the relationship between individual resistances and the equivalent resistance is given by the reciprocal formula, where 1/Req equals the sum of the reciprocals of each individual resistance. This formula is fundamental for analyzing parallel connections in electric circuits.

Algebraic Solution of Circuit Equations

This concept involves using algebraic manipulation to rearrange circuit equations, allowing for the isolation and determination of unknown resistor values. By subtracting known quantities and inverting the equation as needed, one can solve for a missing resistance in a parallel network.

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