Parallel Circuit Physics Example 5

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Example 5

medium
Two resistors (10 Ω10 \text{ } \Omega and 15 Ω15 \text{ } \Omega) are connected in parallel across a 30 V30 \text{ V} supply. Find: (a) total resistance, (b) total current, (c) current through each resistor.

Solution

  1. 1
    (a) 1RT=110+115=330+230=530\frac{1}{R_T} = \frac{1}{10} + \frac{1}{15} = \frac{3}{30} + \frac{2}{30} = \frac{5}{30}, so RT=6 ΩR_T = 6 \text{ } \Omega.
  2. 2
    (b) Itotal=VRT=306=5 AI_{\text{total}} = \frac{V}{R_T} = \frac{30}{6} = 5 \text{ A}.
  3. 3
    (c) I10=3010=3 AI_{10} = \frac{30}{10} = 3 \text{ A}; I15=3015=2 AI_{15} = \frac{30}{15} = 2 \text{ A}. Check: 3+2=5 A3 + 2 = 5 \text{ A}.

Answer

(a)  6 Ω;(b)  5 A;(c)  3 A and 2 A(a)\; 6 \text{ } \Omega; \quad (b)\; 5 \text{ A}; \quad (c)\; 3 \text{ A and } 2 \text{ A}
In parallel, voltage is the same across all branches, but current splits. More current flows through the smaller resistance. The total resistance is always less than the smallest individual resistor.

About Parallel Circuit

A parallel circuit connects components in separate branches between two common nodes, so each component gets the full source voltage.

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