EQUIVALENT RESISTANCES Resistors in Series - Suppose you have three resistors connected in series with one another and a battery as shown. Using K-2 and Ohm’s law: E = + + = IR1 + IR2 + IR3 V1 V2 V3 or E = I(R1 + R2 + R3) Note that the same current would flow if the three resistors were replaced by an equivalent resistance, Req where Req = R1 + R2 + R3 The same argument can be made for any number of resistors connected in series. Req for the n resistors in the sketch at the is given by: Resistors in Parallel - Consider the three resistors connected in parallel with a battery as E. shown. From applying K-2 (and from your lab experiment) it follows that = = = ∆V1 ∆V2 ∆V3 From K-1 and Ohm’s Law: or E I = Note that the same current will flow from the battery if the resistors are replaced by an equivalent resistance Req given by If we have n resistors all connected in parallel the Req is given by At this point try problems 14 through 17 at the back of this unit. ELECTRICAL INSTRUMENTS When a meter (either a voltmeter or ammeter) is introduced into a circuit to make a measurement, it can’t help but change, ever so slightly, the quantity being measured. This is because the meter has some resistance and thus introducing it effects the voltages and currents in the circuit. It should be evident then, that the better the meter, the less it disturbs the circuit. The Galvanometer (symbol: )
EQUIVALENT RESISTANCES Resistors in Series - Suppose you have three resistors connected in series with one another and a battery as shown. Using K-2 and Ohm’s law: E = V1 + V2 + V3 = IR1 + IR2 + IR3 or E = I(R1 + R2 + R3) Note that the same current would flow if the three resistors were replaced by an equivalent resistance, Req where Req = R1 + R2 + R3 The same argument can be made for any number of resistors connected in series. Req for the n resistors in the sketch at the is given by: Resistors in Parallel - Consider the three resistors connected in parallel with a battery as shown. From applying K-2 (and from your lab experiment) it follows that ∆V1 = ∆V2 = ∆V3 = E. From K-1 and Ohm’s Law: or I = E Note that the same current will flow from the battery if the resistors are replaced by an equivalent resistance Req given by If we have n resistors all connected in parallel the Req is given by At this point try problems 14 through 17 at the back of this unit. ELECTRICAL INSTRUMENTS When a meter (either a voltmeter or ammeter) is introduced into a circuit to make a measurement, it can’t help but change, ever so slightly, the quantity being measured. This is because the meter has some resistance and thus introducing it effects the voltages and currents in the circuit. It should be evident then, that the better the meter, the less it disturbs the circuit. The Galvanometer (symbol: )
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