Worksheet: Equivalent Resistance of Resistor Combinations

In this worksheet, we will practice calculating the total resistance of combinations of resistors connected in series and parallel to each other.

Q1:

A 36.0 Ω resistor, a 50.0 Ω resistor, and a 700 Ω resistor are connected together.

What is the largest resistance obtainable?

What is the smallest resistance obtainable?

Q2:

In a car, two 30.0 W power headlights and a 2.40 kW power starter are connected in parallel with each other. A 12.0 V emf battery is connected across these components. What power would one headlight and the starter draw from the battery? Neglect any other resistance in the circuit or in the battery and any change in resistances of the devices.

Q3:

Consider the circuit shown.

Determine the equivalent resistance of the circuit if switch 𝑆 1 is open.

Determine the current drawn from the battery if switch 𝑆 1 is open.

Determine the equivalent resistance of the circuit if switch 𝑆 1 is closed.

Determine the current drawn from the battery if switch 𝑆 1 is closed.

Q4:

Three 300-Ω resistors are connected in series with an AAA battery that has a capacity of 3.0 Amp-Hours.

How long can the battery supply the resistors with power?

If the resistors are connected in parallel, how long can the battery last?

Q5:

What is the equivalent resistance of the series combination of the resistors 𝑅 , 𝑅 1 2 , and 𝑅 3 ?

  • A 𝑅 × 𝑅 × 𝑅 ( 𝑅 + 𝑅 + 𝑅 ) 1 2 3 1 2 3
  • B 1 𝑅 + 1 𝑅 + 1 𝑅 1 2 3
  • C 𝑅 𝑅 + 𝑅 𝑅 + 𝑅 𝑅 1 2 2 3 3 1
  • D 𝑅 + 𝑅 + 𝑅 1 2 3
  • E 𝑅 × 𝑅 × 𝑅 1 2 3

Q6:

What is the equivalent resistance of the parallel combination of the resistors 𝑅 , 𝑅 1 2 , and 𝑅 3 ?

  • A 1 𝑅 + 1 𝑅 + 1 𝑅 1 2 3
  • B 𝑅 + 𝑅 + 𝑅 1 2 3
  • C 𝑅 × 𝑅 × 𝑅 ( 𝑅 + 𝑅 + 𝑅 ) 1 2 3 1 2 3
  • D 𝑅 × 𝑅 × 𝑅 𝑅 × 𝑅 + 𝑅 × 𝑅 + 𝑅 × 𝑅 1 2 3 2 3 1 3 1 2
  • E 𝑅 𝑅 + 𝑅 𝑅 + 𝑅 𝑅 1 2 2 3 3 1

Q7:

What is the value of the current in the circuit shown in the accompanying diagram?

Q8:

What is the resistance of a 4.0 kΩ resistor, a 4.5 kΩ resistor, and a 2.0 kΩ resistor connected in parallel?

Q9:

What is the resistance of a 1.5 kΩ resistor, a 2.5 kΩ resistor, and a 5.0 kΩ resistor connected in series?

Q10:

Two resistors, one having a resistance of 260 Ω, are connected in parallel to produce a total resistance of 110 Ω. What is the value of the second resistance?

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