Current And Resistors 2

Current and Resistors When you connect the terminals of a voltage source to each other, you create a short circuit. This means a high current flow. To limit the current flow, you can use a resistor. The symbol of a resistor is:

Voltage, current and resistance are related to each other as follows: V R = --I V is the voltage across the resistor [unit: volts, or V]; I is the current through the resistor [unit: amperes, or A]; R is the resistance [unit: ohms, or Ω]. Example: Imagine you connect a 1000Ω (or 1kΩ) resistor to a 9V battery. In that case, the current through the resistor (and through the battery of course!) will be: I = V/R = 9V / 1000Ω = 9mA (milli-amps). You can't buy resistors of any value. You can choose from a series of resistors, e.g. the E12 series. The E12 series has the following values: 10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82. If you want other values, you may select one from another (more expensive) series, or create one by connecting multiple resistors in series or parallel.

Resistors in series connection Now we'll connect 3 resistors in series with the battery (see picture on the right). What will be the total resistance of R1, R2 and R3? The voltage across R1 (V1) equals to: V1 = I·R1. And V2 = I·R2, and V3 = I·R3. We know that V1 + V2 + V3 = Vbat, so: Vbat = I·R1 + I·R2 + I·R3 = I·(R1 + R2 + R3). This tells us that the total resistance of resistors is series equals to R1 + R2 + R3 + ..., or:

In this case, the total resistance is 3kΩ. The current I will be: 9V / 3k = 3mA.

Resistors in parallel connection The picture on the right shows a DC voltage source connected with 3 parallel-connected resistors. The question is again: what is the total resistance? The current through R1 (I1) equals to: I1 = Vbat/ R1. And I2 = Vbat/R2, and V3 = Vbat/R3. The total current Itot equals I1 + I2 + I3, so: Itot = Vbat/R1 + Vbat/R2 + Vbat/R3. This proves that the total resistance of parallel connected resistors equals to: 1/Rtot = 1/R1 + 1/R2 + 1/R3 + ... or:

In this case, the total resistance is 333Ω. The total current will be 3 · 9mA = 27mA.

Creating a voltage divider using resistors Take a look at the picture on the right. We see three series connected resistors. We've already learned that the total resistance is 3k. So the current I will be 9V / 3k = 3mA. The voltage at point B, VB, equals 1k·3mA = 3V. (Do you still remember what is meant by 'voltage at point B'? It means: connect the red wire of the volt meter to point B and the black wire to ground.) The general way of calculating the voltage across a resistor in a series connection is: I = Vsource / Rtotal, and Vres = I·R. So:

There are three ways to calculate the voltage at point A: 1. The total resistance of R2 and R3 is 2k, so VA = 2k·3mA = 6V. 2. The voltage across each resistor is 3V, so VA = 6V. 3. Using the equation above: VA = 9V·(2k/3k) = 6V. Does this mean that you can connect your 3V portable cassette player to point B? Well, of course you could, but don't expect it to work! The player acts like a resistor of, say, 50 ohms. That resistor is parallel connected with R3, resulting in a resistance of 47.6 ohms. So VB will drop to 9V·(47.6/2047.6) = 0.2V. And that will never be enough for your player. Conclusion: If you design a voltage divider, don't forget to take the load into account!

Measuring current using a multimeter Most digital multimeters look like this:

1 = Display 2 = Function switch 3 = Transistor socket (optional) 4...6 = Test lead jacks

If you want to measure DC current, set the function switch to the DC current range you want to use. For example, if you expect to measure 1mA, set the switch to 2mA DC. If you have no idea what to expect, set the function switch to the highest DC range available and work down. Having done that, we can connect the test leads. Mulimeters usually come with two test leads: a black one and a red one. To measure current, you need to connect the black test lead to the COM jack and the red lead to the A jack. Connect the other ends of the test leads in series with the load under measurement. If the current flows from red to black, you will read a positive value. Otherwise, a minus sign appears in the display. If you want to measure AC current, set the function switch to the proper AC current range. Connect the test leads in series with device-under-test. Swapping test leads makes no difference (of course!). Note: many meters have a separate jack for measuring high current. Usually the A jack measures up to 200mA. The separate jack will be labeled '20A'. This jack only works when the function switch has been set to 20A. Warning: the 20A jack is usually unfused! Overload may seriously damage your multimeter. Tip: if you want to measure the current flow through a component, you'll have to connect the meter in series with that component. This means you may need to unsolder one end of that component. If the same current also flows though a resistor, you can simply measure the voltage across that resistor and calculate the current. After current measurement, disconnect the leads from the meter. If you forget this and want to measure voltages again, you may cause disasterous shorts!

Measuring resistance using a multimeter If you want to measure resistance, set the function switch to the resistance range you want to use. For example, if you expect the resistance to be 1kΩ, set the switch to 2kΩ. If you have no idea what to expect, set the function switch to the highest DC range available and work down. Having done that, we can connect the test leads. Connect the black test lead to the COM jack and the red lead to the V/Ω jack. Connect the other ends of the test leads across the resistance under measurement.

Please note that in-cicuit measurement may lead to wrong results, since there may be other components parallel-connected to the resistance. It is also a good idea to make sure that the voltage across the resistance is 0V before starting resistance measurement. Also make sure that the equipment-under-test has been turned off!

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