26 Resistors Series (1)
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Problem-Solving Strategy Resistors in Series and Parallel IDENTIFY the relevant concepts: Many resistor networks are made up of resistors in series, in parallel, or a combination of the two. The key concept is that such a network can be replaced by a single equivalent resistor. SET UP the problem using the following steps: 1. Make a drawing of the resistor network. 2. Determine whether the resistors are connected in series or parallel. Note that you can often consider networks such as those in Figs. 26.1c and 26.1d as combinations of series and parallel arrangements. 3. Determine what the target variables are. They could include the equivalent resistance of the network, the potential difference across each resistor, or the current through each resistor. EXECUTE the solution as follows: 1. Use Eq. (26.1) or (26.2) to find the equivalent resistance for a series or a parallel combination, respectively. 2. If the network is more complex, try reducing it to series and parallel combinations. For example, in Fig. 26.1c we first replace the parallel combination of and with its equivalent resistance; this then forms a series combination with In Fig. 26.1d, the combination of and in series forms a parallel combination with 3. When calculating potential differences, remember that when resistors are connected in series, the total potential difference across the combination equals the sum of the individual potential differences. When they are connected in parallel, the potential difference is the same for every resistor and equals the potential difference across the parallel combination.
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Transcript of 26 Resistors Series (1)
Problem-Solving StrategyResistors in Series and Parallel
IDENTIFY the relevant concepts: Many resistor networks are made up of resistors in series, in parallel, or a combination of the two. The key concept is that such a network can be replaced by a single equivalent resistor.
SET UP the problem using the following steps:1. Make a drawing of the resistor network.2. Determine whether the resistors are connected in series or parallel. Note that you can often consider networks such as those in Figs. 26.1c and 26.1d as combinations of series and parallel arrangements.3. Determine what the target variables are. They could include the equivalent resistance of the network, the potential difference across each resistor, or the current through each resistor.
EXECUTE the solution as follows:1. Use Eq. (26.1) or (26.2) to find the equivalent resistance for a series or a parallel combination, respectively.2. If the network is more complex, try reducing it to series and parallel combinations. For example, in Fig. 26.1c we first replace the parallel
combination of and with its equivalent resistance; this then forms a
series combination with In Fig. 26.1d, the combination of and in series forms a parallel combination with
3. When calculating potential differences, remember that when resistors are connected in series, the total potential difference across the combination equals the sum of the individual potential differences. When they are connected in parallel, the potential difference is the same for every resistor and equals the potential difference across the parallel combination.4. Keep in mind the analogous statements for current. When resistors are connected in series, the current is the same through every resistor and equals the current through the series combination. When resistors are connected in parallel, the total current through the combination equals the sum of the currents through the individual resistors.
EVALUATE your answer: Check whether your results are consistent. If resistors are connected in series, the equivalent resistance should be greater than that of any individual resistor; if they are connected in parallel, the equivalent resistance should be less than that of any individual resistor.
