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In the circuit diagram given below, three resistors \(R_1\), \(R_2\) and \(R_3\) of \(5\ Ω\), \(10\ Ω\) and \(20\ Ω\), respectively are connected as shown.
 
9.png
Circuit diagram
 
Calculate,
(a) Current through each resistor
(b) Total current in the circuit
(c) Total resistance in the circuit
 
(a) Since the resistors are connected in parallel, the potential difference across each resistor is same (i.e. \(V = 10V\)). Therefore, the current through each resistor is calculated by the formula,
 
i=ii
 
Current through \(R_1\) \(=\)  \(A\)
 
Current through \(R_2\) \(=\)  \(A\)
 
Current through \(R_3\) \(=\)  \(A\)
 
(b) Total current in the circuit,
 
i=ii+ii+ii
 
On substituting the known current values, we get
 
\(=\)  \(A\)

(c) Total resistance in the circuit,
 
1RP=1Ri+1Ri+1Ri
 
On substituting the known values, we get
 
1RP=iiRP=ii
 
\(=\)  Ω