Practice problems

Transistor switch practice problems

A transistor lets a small current switch a big one: a few milliamps into the base, and up to β times as much through the load. These ten problems start with I_C = β × I_B and work up to sizing a base resistor for a relay and checking how warm a MOSFET runs. Type your answer to check it, and open the working whenever you want it.

The method

I_C = β × I_B

I_B = I_C over β for the smallest base current, with the smallest β on the datasheet
Give the base 2 to 10 times that minimum, so the transistor is fully on (saturated)
R_B = V_control − 0.7 V over I_B, because the base-emitter junction drops about 0.7 V like a diode
Round the base resistor down to a standard value, so the base gets a little more current, not less

Fully on, a transistor keeps only about 0.1 V, and the load's own resistance sets the current. A MOSFET is switched by its gate voltage instead, and fully on it wastes P = I² × R_DS(on).

The problems

Type your answer and tap Check. Every one has the working, step by step.

Problem 1 of 10
A transistor with β = 120 has 0.5 mA flowing into its base, and it isn't fully on yet. What collector current flows?
Show the working
1. Below saturation the collector current is β times the base current: I_C = β × I_B.
2. I_C = 120 × 0.5 mA = 60 mA
Answer: 60 mA
Problem 2 of 10
A relay coil draws 75 mA. The transistor switching it has a β of at least 150. What is the smallest base current that could turn it fully on?
Show the working
1. Work backwards from the load: I_B = I_C over β, with the smallest β, so every part from the batch works.
2. I_B = 75 mA over 150 = 0.5 mA. A real design gives the base 2 to 10 times that.
Answer: 0.5 mA
Problem 3 of 10
A 5 V signal drives a transistor's base through a 2.2 kΩ resistor. The base-emitter junction drops 0.7 V. What base current flows?
Show the working
1. The junction takes 0.7 V, so the resistor gets 5 V − 0.7 V = 4.3 V.
2. I_B = 4.3 V over 2.2 kΩ ≈ 1.95 mA. Volts divided by kilohms gives milliamps.
Answer: 1.95 mA
Problem 4 of 10
A motor draws 250 mA through a transistor whose β is at least 125. You aim for 4 times the minimum base current. What base current do you aim for?
Show the working
1. The minimum is I_B = 250 mA over 125 = 2 mA.
2. Four times that is 4 × 2 mA = 8 mA, so even the weakest transistor is fully on.
Answer: 8 mA
Problem 5 of 10
A 5 V signal feeds a transistor's base through 1 kΩ, and the base-emitter junction drops 0.7 V. The datasheet's smallest β is 80. Up to what load current is the transistor sure to switch fully on?
Show the working
1. First the base current: I_B = 5 V − 0.7 V over 1 kΩ = 4.3 mA.
2. The most collector current that base current can allow is I_C = β × I_B = 80 × 4.3 mA = 344 mA. Any load up to that saturates it.
Answer: 344 mA
Problem 6 of 10
A fully-on transistor switches a 60 Ω load from a 12 V supply, with 0.1 V left across the transistor. What current flows through the load?
Show the working
1. Saturated, the transistor keeps only about 0.1 V, so the load gets 12 V − 0.1 V = 11.9 V.
2. The load itself sets the current: I = 11.9 V over 60 Ω ≈ 0.198 A
3. 0.198 A is 198 mA.
Answer: 198 mA
Problem 7 of 10
A 3.3 V microcontroller pin switches a 150 mA LED strip through an NPN transistor with β of at least 100. The junction drops 0.7 V, and you aim for 3 times the minimum base current. What is the largest base resistor that works?
Show the working
1. The minimum base current is 150 mA over 100 = 1.5 mA, so aim for 3 × 1.5 mA = 4.5 mA.
2. The resistor gets 3.3 V − 0.7 V = 2.6 V.
3. R_B = 2.6 V over 0.0045 A ≈ 578 Ω. Round down to the E12 value 560 Ω, which gives a little more base current, about 4.64 mA.
Answer: 578 Ω
Problem 8 of 10
A 5 V signal switches a 12 V fan drawing 180 mA. The transistor's β is at least 90, the junction drops 0.7 V, and you aim for 5 times the minimum base current. Which E12 resistor do you fit in the base?
Show the working
1. The minimum is 180 mA over 90 = 2 mA, so aim for 5 × 2 mA = 10 mA.
2. R_B = 5 V − 0.7 V over 0.01 A = 430 Ω at most.
3. 430 Ω isn't an E12 value. Round down, because a bigger resistor would starve the base: 390 Ω, giving about 11 mA.
Answer: 390 Ω
Problem 9 of 10
A logic-level MOSFET with an on-resistance R_DS(on) of 0.05 Ω carries 3 A when fully on. How much power does it turn into heat?
Show the working
1. Fully on, a MOSFET acts like a small resistor, so use P = I² × R_DS(on).
2. P = (3 A)² × 0.05 Ω = 9 × 0.05 = 0.45 W
Answer: 0.45 W
Problem 10 of 10
Stretch: a 3.3 V pin drives an NPN that switches a 240 Ω relay coil from 12 V. The transistor keeps 0.1 V when fully on, its β is at least 100, and the junction drops 0.7 V. Aiming for 5 times the minimum base current, what is the largest base resistor, in kilohms?
Show the working
1. The coil's current: I_C = 12 V − 0.1 V over 240 Ω ≈ 49.6 mA.
2. The minimum base current is 49.6 mA over 100 ≈ 0.496 mA, so aim for 5 times that, about 2.48 mA.
3. R_B = 3.3 V − 0.7 V over 2.48 mA ≈ 1.05 kΩ. Round down to the E12 value 1 kΩ: 2.6 mA, about 5.2 times the minimum.
Answer: 1.05 kΩ

Build it in a free lesson

“Transistors as switches” is lesson 5 of 6 in Silicon Ridge, Electronics World 5. Free with an account. Lessons unlock in order, so you’ll do the 32 before it first.

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Try it yourself: free lesson

“Transistors as switches” is lesson 5 of 6 in Silicon Ridge, Electronics World 5. Free with an account. Lessons unlock in order, so you’ll do the 32 before it first.

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The ideas behind it

Questions people ask

Why use the smallest β on the datasheet?

β varies a lot from one transistor to the next, often 100 to 300 for the same part number. Design with the smallest value and every transistor in the batch is fully on. Design with a typical value and some of them sit half on and get hot.

How much extra base current should I give a transistor switch?

Aim for 2 to 10 times the minimum, Ic ÷ β. The extra makes sure the transistor saturates, with only about 0.1 V across it, even when β is low or the load draws a little more than planned. Then round the base resistor down to a standard value, never up.

Does a MOSFET need a base resistor too?

A MOSFET has a gate, not a base, and it's switched by voltage: once the gate is charged, almost no current flows into it. So there's no base current to set. What matters is a gate voltage high enough to turn it fully on, and the heat it makes: P = I² × Rds(on), where Rds(on) is its on-resistance.