A ideal battery is connected to a network consisting of a resistor in series with a…

PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

A 12 V12\,\text{V} ideal battery is connected to a network consisting of a 8 Ω8\,\Omega resistor in series with a branch containing a 4 Ω4\,\Omega resistor in parallel with a 100 μF100\,\mu\text{F} capacitor. The capacitor is initially uncharged. At time t=0t = 0 the switch connecting the battery to the network is closed. (a) Calculate the equivalent resistance seen by the battery during the instant immediately after the switch is closed. (b) Determine the current through the 4 Ω4\,\Omega resistor at that initial instant. (c) Calculate the current through the 4 Ω4\,\Omega resistor after the circuit has reached steady state. (d) Compute the rate at which energy is being dissipated as thermal energy in the 4 Ω4\,\Omega resistor at the initial instant.

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