01 Resistors in Series FINAL

 

 

RESISTORS IN SERIES | CONCEPT OVERVIEW  

The topic of RESITIVITY can be referenced on page 200 of the NCEES Supplied Reference Handbook, 9.3 Version for Computer Based Testing. When multiple RESISTORS are in the same circuit, they are either considered in parallel, in series, or a combination of both. RESISTORS that are connected in SERIES have the same current through each resistor. The properties of RESISTORS IN SERIES can be referenced under the topic of RESISTORS IN SERIES AND PARALLEL on page 200 of the NCEES Supplied Reference Handbook, 9.2 Version for Computer Based Testing.

When resistors are in SERIES, the resistors act like a single resistor whose value is the sum of the resistors:

RS = R1 + R2 + R3 + R 4

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The formula for RESISTORS IN SERIES can be referenced under the topic of RESISTORS IN SERIES AND PARALLEL on page 200 of the NCEES Supplied Reference Handbook, 9.2 Version for Computer Based Testing. Similarly, when resistors are in SERIES, the source voltage is equal to the sum of all the voltages. This relationship is known as KIRCHOFF’S VOLTAGE LAW.

VT = V1 + V2 + V3 + V4 The formula for KIRCHOFF’S VOLTAGE LAW can be referenced under the topic of KIRCHOFF’S LAWS on page 200 of the NCEES Supplied Reference Handbook, 9.2 Version for Computer Based Testing. Applying OHM’S LAW to each resistor yields:

RT =

VT = I(R 1 + R 2 + R 3 + R 4) I

The formula for OHM’S LAW can be referenced under the topic of RESITIVITY on page 200 of the NCEES Supplied Reference Handbook, 9.2 Version for Computer Based Testing. It is important to remember that the current (I) of resistors (R) in series is constant throughout the entire circuit and the voltage drops (V) across each resistor must equal the total voltage supplied to the circuit.   2|PREPINEER.COM    

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CONCEPT EXAMPLE: The circuit below contains 4 resistors that are in series, with a current (I) of 1.0 Amps. Voltage drops across the first, second, and third resistors are given below:

V1 = 5 volts, V2 = 8 volts, V3 = 7 volts . The equivalence resistance of the entire circuit is R EQ = 30 Ω. Find the resistance of each resistor, the voltage drop across the fourth resistor, and the total voltage supplied in the circuit.

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SOLUTION: In this problem we will be utilizing Ohm’s Law, Kirchoff’s Voltage Law, and the properties of resistors in series to solve for the resistance of each resistor in the circuit.

Since the resistors are connected in series, the current (I) remains constant through each resistor. We can use this current value with Ohm’s Law to calculate the resistance of the first, second, and third resistors. In the problem we are given: • Current: I = 1.0 A • Voltage: V1 =5 V, V2 =8 V, V3 =7 V

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Ohm’s law is given as:

V = IR or R =

V I

The formula for OHM’S LAW can be referenced under the topic of RESITIVITY on page 200 of the NCEES Supplied Reference Handbook, 9.2 Version for Computer Based Testing. We can then plug in the given values of the voltage and current to solve for the resistance of the resistor:

R1=

V V1 V , R 2= 2 , R 3= 3 I I I

R1=

5.0V 8.0V 7.0V =5.0 ! , R 2 = =8.0 !, R 3 = 7.0 ! 1.0A 1.0A 1.0A

We are given the equivalent resistance, which we can use to find the resistance of the fourth resistor.

R EQ = R 1 + R 2 + R 3 + R 4 The formula for RESISTORS IN series can be referenced under the topic of RESISTORS IN SERIES AND PARALLEL on page 200 of the NCEES Supplied Reference Handbook,   5|PREPINEER.COM    

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9.2 Version for Computer Based Testing. Since we are given the equivalent resistance, and already solved for the resistance in the first, second, and third resistors, we can solve for the resistance across the fourth resistor.

R EQ = 30 Ω R 1 =5.0 ! , R 2 =8.0 !, R 3 =7.0 !

Now, using the equivalent resistance, we can find the resistance across the fourth resistor. This is a series circuit, so the equivalent resistance is the sum of the individual resistances.

R 4 = R EQ − (R 1 + R 2 + R 3 ) R 4 = 30Ω − (5.0Ω + 8.0Ω + 7.0Ω) = 10.0Ω

Since the current is constant (I=1.0A),, we can use Ohm’s Law to find the voltage:

V4 = I x R 4 The formula for OHM’S LAW can be referenced under the topic of RESITIVITY on page 200 of the NCEES Supplied Reference Handbook, 9.2 Version for Computer Based   6|PREPINEER.COM    

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Testing.

V4 = (1.0A)(10Ω) = 10V The total voltage supplied by the battery must equal to the total voltage drop across the circuit (Kirchhoff's Voltage Law). So, we must sum up the voltage drops across the resistors.

V = V1 + V2 + V3 + V4 The formula for KIRCHOFF’S VOLTAGE LAW can be referenced under the topic of KIRCHOFF’S LAWS on page 200 of the NCEES Supplied Reference Handbook, 9.2 Version for Computer Based Testing.

V = 5.0 + 8.0 + 7.0 + 10.0 = 30.0V

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