# Lesson 4 Flashcards — Series, Parallel, and Dividers

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<summary><strong>1. What makes two elements in series? In parallel?</strong></summary>
<div class="card-answer"><p><strong>Series</strong> elements carry the <em>same current</em> — end to end with nothing branching between them. <strong>Parallel</strong> elements share the <em>same two nodes</em>, so they see the same voltage.</p></div>
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<summary><strong>2. Give the equivalent resistance for resistors in series and in parallel.</strong></summary>
<div class="card-answer"><p>Series: <span class="math notranslate nohighlight">\(R_\text{EQ} = R_1 + R_2 + \cdots\)</span>. Parallel: <span class="math notranslate nohighlight">\(1/R_\text{EQ} = 1/R_1 + 1/R_2 + \cdots\)</span>, or for exactly two, <span class="math notranslate nohighlight">\(R_\text{EQ} = R_1R_2/(R_1+R_2)\)</span>.</p></div>
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<summary><strong>3. How can you sanity-check a parallel combination?</strong></summary>
<div class="card-answer"><p>The result is always <strong>smaller than the smallest branch</strong>. If it is not, you made an arithmetic error.</p></div>
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<summary><strong>4. State the voltage divider rule.</strong></summary>
<div class="card-answer"><p><span class="math notranslate nohighlight">\(V_k = V_s \cdot R_k / R_\text{EQ}\)</span> — each resistor takes a share proportional to <em>its own</em> resistance. The biggest resistor gets the biggest voltage.</p></div>
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<summary><strong>5. State the current divider rule.</strong></summary>
<div class="card-answer"><p>The general rule works for any number of parallel branches: <span class="math notranslate nohighlight">\(I_X = (R_\text{EQ,par}/R_X)\,I_\text{total}\)</span>, where <span class="math notranslate nohighlight">\(R_\text{EQ,par}\)</span> is the equivalent of the parallel group and the branch's <em>own</em> resistance sits in the <strong>denominator</strong>. Substituting <span class="math notranslate nohighlight">\(R_\text{EQ,par} = R_1R_2/(R_1+R_2)\)</span> gives the familiar two-branch form, <span class="math notranslate nohighlight">\(I_1 = I_\text{total}\cdot R_2/(R_1+R_2)\)</span>, where the <em>other</em> resistor's value sits in the numerator because current prefers the easier path.</p></div>
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<summary><strong>6. What is a classic Quiz 1 error with the current divider?</strong></summary>
<div class="card-answer"><p>Reaching for the two-branch <strong>swap</strong> form when there are three or more branches — it is only valid for exactly two. With three or more, find <span class="math notranslate nohighlight">\(R_\text{EQ,par}\)</span> and use the general rule, keeping the branch's own resistance in the <strong>denominator</strong>. The two rules are mirror images: the voltage divider puts the element's own R on top, the general current divider puts it on the bottom.</p></div>
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<summary><strong>7. Why does adding loads in parallel risk overloading a circuit?</strong></summary>
<div class="card-answer"><p>Each added branch <em>lowers</em> <span class="math notranslate nohighlight">\(R_\text{EQ}\)</span>, which <em>raises</em> the current drawn from the source. That is exactly how a circuit gets overloaded.</p></div>
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<summary><strong>8. Why are the outlets in a building wired in parallel?</strong></summary>
<div class="card-answer"><p>So every outlet sees the same 120 V (an AC value — defined properly in Lesson 6), and so unplugging one device does not interrupt the others. Old series Christmas lights show the alternative: one bulb fails and the whole string goes dark.</p></div>
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<summary><strong>9. Describe the reduce-solve-expand method.</strong></summary>
<div class="card-answer"><p>Label nodes, collapse series and parallel groups working <em>back toward the source</em> (redrawing each time), find <span class="math notranslate nohighlight">\(I_s = V_s/R_\text{EQ}\)</span>, then expand outward with the divider rules to get the quantity asked for.</p></div>
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<summary><strong>10. Why redraw the circuit after every reduction step?</strong></summary>
<div class="card-answer"><p>Because it is far faster than finding a wrong answer later. Most reduction errors come from misreading which elements are still in parallel after a previous step.</p></div>
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