Three resistors of resistances 5ohm, 10ohms and 20ohms are connected parallel to a battery
of 12V. Calculate;
a) The current through each resistor.
b) The total current in the circuit.
c) Total resistance in the circuit.
Answers
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Answer:
Explanation:
Given :
- R¹ = 5 Ω , R² = 10 Ω , R³ = 20 Ω are connected in parallel combination.
- Volt (v) = 12 V
To Find :
- I) The current through each resistor.
- II) The total current in the circuit.
- III) Total resistance in the circuit.
Formula to be used :
- Ohms law formula, .ie,, V = IR
- Total current formula, ie,, I = I¹ + I² + l³
If resistance is connected in parallel, the parallel resistance is given by :-
- 1/Rp = 1/R1 + 1/R2 + 1/R3 + 1/R4,...1/Rn
Solution :
★Case(I), The current through each resistor.
I¹ = V/R¹
⇒I¹ = 12/5
⇒I¹ = 2.4 A★
I² = V/R²
⇒ I² = 12/10
⇒ I² = 1.2 A★
I³ = V/R³
⇒ I³ = 12/20
⇒ I³ = 0.6 A★
★Case(II), The total current in the circuit.
I = I¹ + l² + l³
⇒ I = 2.4 + 1.2 + 0.6
⇒ I = 3.6 + 0.6
⇒ I = 4.2 A★
★Case(III), Total resistance in the circuit.
1/Rp = 1/R1 + 1/R2 + 1/R3
⇒ 1/Rp = 1/5 + 1/10 + 1/20
⇒ 1/Rp = 5 + 10 + 20/5 × 10 × 20
⇒ 1/Rp = 35/1000
⇒ 1/Rp = 0.035 Ω★
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