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Introduction to SAT II Physics - FreeExamPapers

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However, each resis<strong>to</strong>r causes a voltage drop, and if there is more than one resis<strong>to</strong>r in the<br />

circuit, the sum of the voltage drops across each resis<strong>to</strong>r in the circuit is equal <strong>to</strong> the <strong>to</strong>tal<br />

voltage drop in the circuit. The <strong>to</strong>tal resistance in a circuit with two or more resis<strong>to</strong>rs in<br />

series is equal <strong>to</strong> the sum of the resistance of all the resis<strong>to</strong>rs: a circuit would have the<br />

same resistance if it had three resis<strong>to</strong>rs in series, or just one big resis<strong>to</strong>r with the<br />

resistance of the original three resis<strong>to</strong>rs put <strong>to</strong>gether. In equation form, this principle is<br />

quite simple. In a circuit with two resis<strong>to</strong>rs, and , in series, the <strong>to</strong>tal resistance,<br />

is:<br />

EXAMPLE<br />

In the figure above, a battery supplies 30 V <strong>to</strong> a circuit with a 10 resis<strong>to</strong>r and a 20<br />

resis<strong>to</strong>r. What is the current in the circuit, and what is the voltage drop across each resis<strong>to</strong>r?<br />

WHAT IS THE CURRENT IN THE CIRCUIT?<br />

We can determine the current in the circuit by applying Ohm’s Law: I = V/R. We know<br />

what V is, but we need <strong>to</strong> calculate the <strong>to</strong>tal resistance in the circuit by adding <strong>to</strong>gether<br />

the individual resistances of the two resis<strong>to</strong>rs in series:<br />

When we know the <strong>to</strong>tal resistance in the circuit, we can determine the current through<br />

the circuit with a simple application of Ohm’s Law:<br />

WHAT IS THE VOLTAGE DROP ACROSS EACH RESISTOR?<br />

Determining the voltage drop across an individual resis<strong>to</strong>r in a series of resis<strong>to</strong>rs simply<br />

requires a reapplication of Ohm’s Law. We know the current through the circuit, and we<br />

know the resistance of that individual resis<strong>to</strong>r, so the voltage drop across that resis<strong>to</strong>r is<br />

225

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