Question
Consider the circuit shown below. Does the analysis of the circuit require Kirchhoff's method, or can it be redrawn to simplify the circuit? If it is a circuit of series and parallel connections, what is the equivalent resistance?
Step 1
The equivalent resistance of a series connection is the sum of the resistances. So, we have: \[R_{3,5}=R_3+R_5\] Show more…
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What is the answer
Circuits. If two resistors are connected in parallel, the combined resistance is given by the formula $R=\frac{1}{1 / R_{1}+1 / R_{2}}$ where $R_{1}$ and $R_{2}$ are the individual resistances. Simplify the formula.
Prerequisites and Review
RATIONAL EXPRESSIONS
In the resonant circuit of the figure the dissipative element is a resistor $R^{\prime}$ connected in parallel, rather than in series, with the $L C$ combination. Work out the equation, analogous to Eq. 2, which applies to this circuit. Find also the conditions on the solution analogous to those that hold in the series $R L C$ circuit. If a series $R L C$ and a parallel $R^{\prime} L C$ circuit have the same $L, C$, and $Q$. how must $R^{\prime}$ be related to $R ?$
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